In the present paper,we build the new analytical exact solutions of a nonlinear differential equation,specifically,coupled Boussinesq-Burgers equations by means of Exp-function method.Then,we analyze the results by pl...In the present paper,we build the new analytical exact solutions of a nonlinear differential equation,specifically,coupled Boussinesq-Burgers equations by means of Exp-function method.Then,we analyze the results by plotting the three dimensional soliton graphs for each case,which exhibit the simplicity and effectiveness of the proposed method.The primary purpose of this paper is to employ a new approach,which allows us victorious and efficient derivation of the new analytical exact solutions for the coupled Boussinesq-Burgers equations.展开更多
The ophiolite suite from south Andaman Islands forms part of the Tethyan Ophiolite Belt and preserves the remnants of an ideal ophiolite sequence comprising a basal serpentinized and tectonised mantle peridotite follo...The ophiolite suite from south Andaman Islands forms part of the Tethyan Ophiolite Belt and preserves the remnants of an ideal ophiolite sequence comprising a basal serpentinized and tectonised mantle peridotite followed by ultramafic and mafic cumulate units, basaltic dykes and spilitic pillow basalts interlayered with arkosic wacke. Here, we present new major, trace, rare earth(REE) and platinum group(PGE) element data for serpentinized and metasomatized peridotites(dunites) exposed in south Andaman representing the tectonized mantle section of the ophiolite suite. Geochemical features of the studied rocks, marked by Al_2 O_3/TiO_2 > 23, LILE-LREE enrichment, HFSE depletion, and U-shaped chondrite-normalized REE patterns with(La/Sm)N > 1 and(Gd/Yb)N <1, suggest contributions from boninitic mantle melts. These observations substantiate a subduction initiation process ensued by rapid slab roll-back with extension and seafloor spreading in an intraoceanic fore-arc regime. The boninitic composition of the serpentinized peridotites corroborate fluid and melt interaction with mantle manifested in terms of(i) hydration, metasomatism and serpentinization of depleted, MORB-type, sub-arc wedge mantle residual after repeated melt extraction; and(ii) refertilization of refractory mantle peridotite by boninitic melts derived at the initial stage of intraoceanic subduction. Serpentinized and metasomatized mantle dunites in this study record both MOR and intraoceanic arc signatures collectively suggesting suprasubduction zone affinity. The elevated abundances of Pd(4.4-12.2 ppb) with highΣPPGE/∑IPGE(2-3) and Pd/Ir(2-5.5) ratios are in accordance with extensive melt-rock interaction through percolation of boninitic melts enriched in fluid-fluxed LILE-LREE into the depleted mantle after multiple episodes of melt extraction. The high Pd contents with relatively lower Ir concentrations of the samples are analogous to characteristic PGE signatures of boninitic magmas and might have resulted by the infiltration of boninitic melt展开更多
The present paper deals with two reliable efficient methods viz.tanh-sech method and modified Kudryashov method,which are used to solve time-fractional nonlinear evolution equation.For delineating the legitimacy of pr...The present paper deals with two reliable efficient methods viz.tanh-sech method and modified Kudryashov method,which are used to solve time-fractional nonlinear evolution equation.For delineating the legitimacy of proposed methods,we employ it to the time-fractional fifth-order modified Sawada-Kotera equations.As a consequence,we effectively obtained more new exact solutions for time-fractional fifth-order modified Sawada-Kotera equation.We have also presented the numerical simulations for time-fractional fifth-order modified Sawada-Kotera equation by means of three dimensional plots.展开更多
This article considers time-dependent variable coefficients(2+1)and(3+1)-dimensional extended Sakovich equation.Painlevéanalysis and auto-Bäcklund transformation methods are used to examine both the consider...This article considers time-dependent variable coefficients(2+1)and(3+1)-dimensional extended Sakovich equation.Painlevéanalysis and auto-Bäcklund transformation methods are used to examine both the considered equations.Painlevéanalysis is appeared to test the integrability while an auto-Bäcklund transformation method is being presented to derive new analytic soliton solution families for both the considered equations.Two new family of exact analytical solutions are being obtained success-fully for each of the considered equations.The soliton solutions in the form of rational and exponential functions are being depicted.The results are also expressed graphically to illustrate the potential and physical behaviour of both equations.Both the considered equations have applications in ocean wave theory as they depict new solitary wave soliton solutions by 3D and 2D graphs.展开更多
In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov （KdV-KZK） equa- tion are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For thi...In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov （KdV-KZK） equa- tion are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the non- linear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.展开更多
In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetso...In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetsov(m ZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie's modified Riemann–Liouville sense.展开更多
In this paper, numerical solutions of the stochastic Fisher equation have been obtained by using a semi-implicit finite difference scheme. The samples for the Wiener process have been obtained from cylindrical Wiener ...In this paper, numerical solutions of the stochastic Fisher equation have been obtained by using a semi-implicit finite difference scheme. The samples for the Wiener process have been obtained from cylindrical Wiener process and Q-Wiener process. Stability and convergence of the proposed finite difference scheme have been discussed scrupulously. The sample paths obtained from cylindrical Wiener process and Q-Wiener process have also been shown graphically.展开更多
In the present paper the Riesz fractional coupled Schr6dinger-Boussinesq （S-B） equations have been solved by the time-splitting Fourier spectral （TSFS） method. This proposed technique is utilized for discretizing ...In the present paper the Riesz fractional coupled Schr6dinger-Boussinesq （S-B） equations have been solved by the time-splitting Fourier spectral （TSFS） method. This proposed technique is utilized for discretizing the Schrodinger like equation and further, a pseudospectral discretization has been employed for the Boussinesq-like equation. Apart from that an implicit finite difference approach has also been proposed to compare the results with the solutions obtained from the time-splitting technique. Furthermore, the time-splitting method is proved to be unconditionally stable. The error norms along with the graphical solutions have also been presented here.展开更多
Objective:To study the in vivo efficacy of these two ACTs in the treatment of Plasmodium falciparum {P.falciparum malaria) in Kolkata and to detennine the prevalence of mutant S769N codon of the PfATPase6 gene among f...Objective:To study the in vivo efficacy of these two ACTs in the treatment of Plasmodium falciparum {P.falciparum malaria) in Kolkata and to detennine the prevalence of mutant S769N codon of the PfATPase6 gene among field isolates of P.falciparum collected from the study area. Methods:A total of 207 P.falciparum positive cases were enrolled randomly in two study arms and followed up for 42 days as per WHO(2009) protocol.A portion of PfATPase6 gene spanning codon S769N was amplified and sequenced by direct sequencing method.Results:It was observed that the efficacy of bodi the ACT regimens were highly effective in the study area and no mutant S769N was detected from any isolate.Conclusions:The used,combination AS+SP is effective and the other combination AM+I.F might be an alternative,if needed.展开更多
In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stoch...In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stochastic Kudryashov–Sinelshchikov equation to deterministic partial differential equation. Also we have applied inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space.展开更多
Externality;the term can define as a positive or negative impact from either production or consumption of goods or services.Services provided by particular location have very specific dependency on spatial characteris...Externality;the term can define as a positive or negative impact from either production or consumption of goods or services.Services provided by particular location have very specific dependency on spatial characteristics of that region.A region’s distinct characteristics make it ecologically unique from other such regions.Ecosystem services are offered by these regions thus differ according to these unique ecological features.In this particular study,artificially imposed expansion of coastal shrimp farming towards the inland and its impact over paddy cultivation have been addressed.Optimization of the extent of this manipulative coastal expansion has been supported by little modification of a previously described model.Here the investment prediction for both shrimp and paddy farming has been investigated by calculating net present value(NPV).Shrimp farming has very specific externality on local ecosystem services.In this particular case,some contradictory results are presented and with respect to positive or negative externality;but the externalities are strong.NPV results indicate that there is no long-term profitability in case of shrimp farming.Hence,an overall externality of shrimp farming has been described in context of this study.展开更多
Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been anal...Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been analyzed. The efficiency of the proposed higher-order approximation scheme has been discussed in the results section. The solutions of SPKEs in the presence of Newtonian temperature feedback have also been provided to further discuss the physical behavior of the fractional model.展开更多
In this work, we examine two algorithm schemes, namely, Kudryashov expansion and Auxiliary equation method for obtaining new optical soliton solutions of the discrete electrical lattice models in nonlinear scheme(Sale...In this work, we examine two algorithm schemes, namely, Kudryashov expansion and Auxiliary equation method for obtaining new optical soliton solutions of the discrete electrical lattice models in nonlinear scheme(Salerno equation). Our solutions obtained here are include the hyperbolic, rational, and trigonometric functions. Our two used methods are proved to be effective and powerful methods in obtaining the exact solutions of nonlinear evolution equations(NLEEs).展开更多
In this paper,time-fractional Sharma-Tasso-Olver(STO)equation has been solved numerically through the Petrov-Galerkin approach utilizing a quintic B-spline function as the test function and a linear hat function as th...In this paper,time-fractional Sharma-Tasso-Olver(STO)equation has been solved numerically through the Petrov-Galerkin approach utilizing a quintic B-spline function as the test function and a linear hat function as the trial function.The Petrov-Galerkin technique is effectively implemented to the fractional STO equation for acquiring the approximate solution numerically.The numerical outcomes are observed in adequate compatibility with those obtained from variational iteration method(VIM)and exact solutions.For fractional order,the numerical outcomes of fractional Sharma-Tasso-Olver equations are also compared with those obtained by variational iteration method(VIM)in Song et al.[Song L.,Wang Q.,Zhang H.,Rational approximation solution of the fractional Sharma-Tasso-Olver equation,J.Comput.Appl.Math.224:210-218,2009].Numerical experiments exhibit the accuracy and efficiency of the approach in order to solve nonlinear fractional STO equation.展开更多
文摘In the present paper,we build the new analytical exact solutions of a nonlinear differential equation,specifically,coupled Boussinesq-Burgers equations by means of Exp-function method.Then,we analyze the results by plotting the three dimensional soliton graphs for each case,which exhibit the simplicity and effectiveness of the proposed method.The primary purpose of this paper is to employ a new approach,which allows us victorious and efficient derivation of the new analytical exact solutions for the coupled Boussinesq-Burgers equations.
基金the funds from Council of Scientific and Industrial Research(CSIR)to CSIR-National Institute of Oceanography through the MLP-1703 and GAP 2175 projectsupported by Foreign Expert funding from CUGB and Professorial position at the Adelaide University
文摘The ophiolite suite from south Andaman Islands forms part of the Tethyan Ophiolite Belt and preserves the remnants of an ideal ophiolite sequence comprising a basal serpentinized and tectonised mantle peridotite followed by ultramafic and mafic cumulate units, basaltic dykes and spilitic pillow basalts interlayered with arkosic wacke. Here, we present new major, trace, rare earth(REE) and platinum group(PGE) element data for serpentinized and metasomatized peridotites(dunites) exposed in south Andaman representing the tectonized mantle section of the ophiolite suite. Geochemical features of the studied rocks, marked by Al_2 O_3/TiO_2 > 23, LILE-LREE enrichment, HFSE depletion, and U-shaped chondrite-normalized REE patterns with(La/Sm)N > 1 and(Gd/Yb)N <1, suggest contributions from boninitic mantle melts. These observations substantiate a subduction initiation process ensued by rapid slab roll-back with extension and seafloor spreading in an intraoceanic fore-arc regime. The boninitic composition of the serpentinized peridotites corroborate fluid and melt interaction with mantle manifested in terms of(i) hydration, metasomatism and serpentinization of depleted, MORB-type, sub-arc wedge mantle residual after repeated melt extraction; and(ii) refertilization of refractory mantle peridotite by boninitic melts derived at the initial stage of intraoceanic subduction. Serpentinized and metasomatized mantle dunites in this study record both MOR and intraoceanic arc signatures collectively suggesting suprasubduction zone affinity. The elevated abundances of Pd(4.4-12.2 ppb) with highΣPPGE/∑IPGE(2-3) and Pd/Ir(2-5.5) ratios are in accordance with extensive melt-rock interaction through percolation of boninitic melts enriched in fluid-fluxed LILE-LREE into the depleted mantle after multiple episodes of melt extraction. The high Pd contents with relatively lower Ir concentrations of the samples are analogous to characteristic PGE signatures of boninitic magmas and might have resulted by the infiltration of boninitic melt
文摘The present paper deals with two reliable efficient methods viz.tanh-sech method and modified Kudryashov method,which are used to solve time-fractional nonlinear evolution equation.For delineating the legitimacy of proposed methods,we employ it to the time-fractional fifth-order modified Sawada-Kotera equations.As a consequence,we effectively obtained more new exact solutions for time-fractional fifth-order modified Sawada-Kotera equation.We have also presented the numerical simulations for time-fractional fifth-order modified Sawada-Kotera equation by means of three dimensional plots.
文摘This article considers time-dependent variable coefficients(2+1)and(3+1)-dimensional extended Sakovich equation.Painlevéanalysis and auto-Bäcklund transformation methods are used to examine both the considered equations.Painlevéanalysis is appeared to test the integrability while an auto-Bäcklund transformation method is being presented to derive new analytic soliton solution families for both the considered equations.Two new family of exact analytical solutions are being obtained success-fully for each of the considered equations.The soliton solutions in the form of rational and exponential functions are being depicted.The results are also expressed graphically to illustrate the potential and physical behaviour of both equations.Both the considered equations have applications in ocean wave theory as they depict new solitary wave soliton solutions by 3D and 2D graphs.
文摘In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov （KdV-KZK） equa- tion are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the non- linear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.
基金Supported by BRNS of Bhaba Atomic Research Centre,Mumbai under Department of Atomic Energy,Government of India vide under Grant No.2012/37P/54/BRNS/2382
文摘In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetsov(m ZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie's modified Riemann–Liouville sense.
文摘In this paper, numerical solutions of the stochastic Fisher equation have been obtained by using a semi-implicit finite difference scheme. The samples for the Wiener process have been obtained from cylindrical Wiener process and Q-Wiener process. Stability and convergence of the proposed finite difference scheme have been discussed scrupulously. The sample paths obtained from cylindrical Wiener process and Q-Wiener process have also been shown graphically.
基金Supported by NBHM,Mumbai,under Department of Atomic Energy,Government of India vide Grant No.2/48(7)/2015/NBHM(R.P.)/R&D Ⅱ/11403
文摘In the present paper the Riesz fractional coupled Schr6dinger-Boussinesq （S-B） equations have been solved by the time-splitting Fourier spectral （TSFS） method. This proposed technique is utilized for discretizing the Schrodinger like equation and further, a pseudospectral discretization has been employed for the Boussinesq-like equation. Apart from that an implicit finite difference approach has also been proposed to compare the results with the solutions obtained from the time-splitting technique. Furthermore, the time-splitting method is proved to be unconditionally stable. The error norms along with the graphical solutions have also been presented here.
基金the Department of Health and Family Welfare,Government of West Bengal,India for funding the project
文摘Objective:To study the in vivo efficacy of these two ACTs in the treatment of Plasmodium falciparum {P.falciparum malaria) in Kolkata and to detennine the prevalence of mutant S769N codon of the PfATPase6 gene among field isolates of P.falciparum collected from the study area. Methods:A total of 207 P.falciparum positive cases were enrolled randomly in two study arms and followed up for 42 days as per WHO(2009) protocol.A portion of PfATPase6 gene spanning codon S769N was amplified and sequenced by direct sequencing method.Results:It was observed that the efficacy of bodi the ACT regimens were highly effective in the study area and no mutant S769N was detected from any isolate.Conclusions:The used,combination AS+SP is effective and the other combination AM+I.F might be an alternative,if needed.
文摘In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stochastic Kudryashov–Sinelshchikov equation to deterministic partial differential equation. Also we have applied inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space.
基金University Grants Commission(UGC)NET fellowship[Ref No.F.16-6(DEC.2016)/2017(NET)]University Grants Commission(UGC)for D S Kothari fellowship reference no.BL/17-18/0490.
文摘Externality;the term can define as a positive or negative impact from either production or consumption of goods or services.Services provided by particular location have very specific dependency on spatial characteristics of that region.A region’s distinct characteristics make it ecologically unique from other such regions.Ecosystem services are offered by these regions thus differ according to these unique ecological features.In this particular study,artificially imposed expansion of coastal shrimp farming towards the inland and its impact over paddy cultivation have been addressed.Optimization of the extent of this manipulative coastal expansion has been supported by little modification of a previously described model.Here the investment prediction for both shrimp and paddy farming has been investigated by calculating net present value(NPV).Shrimp farming has very specific externality on local ecosystem services.In this particular case,some contradictory results are presented and with respect to positive or negative externality;but the externalities are strong.NPV results indicate that there is no long-term profitability in case of shrimp farming.Hence,an overall externality of shrimp farming has been described in context of this study.
文摘Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been analyzed. The efficiency of the proposed higher-order approximation scheme has been discussed in the results section. The solutions of SPKEs in the presence of Newtonian temperature feedback have also been provided to further discuss the physical behavior of the fractional model.
文摘In this work, we examine two algorithm schemes, namely, Kudryashov expansion and Auxiliary equation method for obtaining new optical soliton solutions of the discrete electrical lattice models in nonlinear scheme(Salerno equation). Our solutions obtained here are include the hyperbolic, rational, and trigonometric functions. Our two used methods are proved to be effective and powerful methods in obtaining the exact solutions of nonlinear evolution equations(NLEEs).
文摘In this paper,time-fractional Sharma-Tasso-Olver(STO)equation has been solved numerically through the Petrov-Galerkin approach utilizing a quintic B-spline function as the test function and a linear hat function as the trial function.The Petrov-Galerkin technique is effectively implemented to the fractional STO equation for acquiring the approximate solution numerically.The numerical outcomes are observed in adequate compatibility with those obtained from variational iteration method(VIM)and exact solutions.For fractional order,the numerical outcomes of fractional Sharma-Tasso-Olver equations are also compared with those obtained by variational iteration method(VIM)in Song et al.[Song L.,Wang Q.,Zhang H.,Rational approximation solution of the fractional Sharma-Tasso-Olver equation,J.Comput.Appl.Math.224:210-218,2009].Numerical experiments exhibit the accuracy and efficiency of the approach in order to solve nonlinear fractional STO equation.
