Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhom...Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhomogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero- Degasperis-Focas equation.展开更多
A new method is proposed to numerically simulate problems of trains passing by each other at the same speed, and is implemented in UDF language of commercial software Fluent. Because only a half of the computational d...A new method is proposed to numerically simulate problems of trains passing by each other at the same speed, and is implemented in UDF language of commercial software Fluent. Because only a half of the computational domain is required and the dynamic mesh technique is avoided, the computational efficiency is greatly improved. A two-dimensional test case is used for validation, which shows that the flow field and the pressure wave during the train-passing events can be correctly calculated by this new method. This method can be easily extended to three-dimensional simulations, to deal with practical problems.展开更多
A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such no...A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such nonlinear wave equations admit richer classical and nonclassical symmetries, leading to the conservation laws and the reduction of the wave equations. Some exact solutions of the considered wave equations for particular cases are derived.展开更多
Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2...Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.展开更多
A(2+1)-dimensional modified KdV(2DmKdV)system is considered from several perspectives.Firstly,residue symmetry,a type of nonlocal symmetry,and the Bäcklund transformation are obtained via the truncated Painlev...A(2+1)-dimensional modified KdV(2DmKdV)system is considered from several perspectives.Firstly,residue symmetry,a type of nonlocal symmetry,and the Bäcklund transformation are obtained via the truncated Painlevéexpansion method.Subsequently,the residue symmetry is localized to a Lie point symmetry of a prolonged system,from which the finite transformation group is derived.Secondly,the integrability of the 2DmKdV system is examined under the sense of consistent tanh expansion solvability.Simultaneously,explicit soliton-cnoidal wave solutions are provided.Finally,abundant patterns of soliton molecules are presented by imposing the velocity resonance condition on the multiple-soliton solution.展开更多
The kagome superconductor CsV_(3)Sb_(5) has attracted widespread attention due to its rich correlated electron states including superconductivity, charge density wave(CDW), nematicity, and pair density wave. Notably, ...The kagome superconductor CsV_(3)Sb_(5) has attracted widespread attention due to its rich correlated electron states including superconductivity, charge density wave(CDW), nematicity, and pair density wave. Notably, the modulation of the intertwined electronic orders by the chemical doping is significant to illuminate the cooperation/competition between multiple phases in kagome superconductors. In this study, we have synthesized a series of tantalum-substituted Cs(V_(1-x)Ta_(x))_(3)Sb_(5) by a modified self-flux method. Electrical transport measurements reveal that CDW is suppressed gradually and becomes undetectable as the doping content of x is over 0.07. Concurrently, the superconductivity is enhanced monotonically from T_(c) ~ 2.8 K at x = 0 to 5.2 K at x = 0.12. Intriguingly, in the absence of CDW, Cs(V_(1-x)Ta_(x))_(3)Sb_(5)(x = 0.12) crystals exhibit a pronounced two-fold symmetry of the in-plane angular-dependent magnetoresistance(AMR) in the superconducting state, indicating the anisotropic superconducting properties in the Cs(V_(1-x)Ta_(x))_(3)Sb_(5). Our findings demonstrate that Cs(V_(1-x)Ta_(x))_(3)Sb_(5) with the non-trivial band topology is an excellent platform to explore the superconductivity mechanism and intertwined electronic orders in quantum materials.展开更多
Applying the consistent Riccati expansion method, the extended(2+1)-dimensional shallow water wave equation is proved consistent Riccati solvable and the exact interaction solutions including soliton-cnoidal wave solu...Applying the consistent Riccati expansion method, the extended(2+1)-dimensional shallow water wave equation is proved consistent Riccati solvable and the exact interaction solutions including soliton-cnoidal wave solutions,solitoff-typed solutions are obtained. With the help of the truncated Painlev′e expansion, the corresponding nonlocal symmetry is also given, and furthermore, the nonlocal symmetry is localized by prolonging the related enlarged system.展开更多
As a controllable alternative to cavitation collapse-induced shock waves,numerous cavitation studies on laser-induced breakdown have been carried out in hydromechanics.When the laser focusing region is not spherical,t...As a controllable alternative to cavitation collapse-induced shock waves,numerous cavitation studies on laser-induced breakdown have been carried out in hydromechanics.When the laser focusing region is not spherical,the shock waves caused by laser breakdown also exhibit non-spherical symmetry propagation.Recently,some researchers have proposed the linear superposition theory based on the far field measurement data to explain this asymmetry,assuming that it is essentially the linear superposition of multiple wave fronts caused by multiple points of laser-induced breakdown that leads to the asymmetric propagation of shock waves.In this study,measurements of shock wave propagation processes with different breakdown energies are carried out based on a nanosecond resolution photogrammetry system,and the propagation velocities of shock waves in different directions are directly measured using a double exposure technique on a single frame.In the experiment,the velocity of the shock wave at the beginning of the breakdown was measured up to nearly 4000 m/s.The early shock wave front was ellipsoidal,and the propagation velocity in the laser incident direction was generally slower than that in the perpendicular direction,decaying to the speed of sound in water within 1000 ns after the breakdown,and the wave front gradually approached to a circle.The variability of the shock wave front pressure ratio in the laser propagation direction and the vertical direction implies that the linear superposition theory applicable to the far field is not applicable to the near field.There may be more complex mechanism for the near-field shock wave propagation process.展开更多
In this paper,the truncated Painlev′e analysis,nonlocal symmetry,Bcklund transformation of the（2＋1）-dimensional modified Bogoyavlenskii–Schiff equation are presented.Then the nonlocal symmetry is localized to the...In this paper,the truncated Painlev′e analysis,nonlocal symmetry,Bcklund transformation of the（2＋1）-dimensional modified Bogoyavlenskii–Schiff equation are presented.Then the nonlocal symmetry is localized to the corresponding nonlocal group by the prolonged system.In addition,the（2＋1）-dimensional modified Bogoyavlenskii–Schiff is proved consistent Riccati expansion（CRE） solvable.As a result,the soliton–cnoidal wave interaction solutions of the equation are explicitly given,which are difficult to find by other traditional methods.Moreover figures are given out to show the properties of the explicit analytic interaction solutions.展开更多
Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of t...Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of the two equations are obtained. The CRE method is applied to the two equations to obtain new B?cklund transformations from which a type of interesting interaction solution between solitons and periodic waves is generated.展开更多
We suggest a new family of Co[Ni-based materials that may host unconventional high temperature superconductivity （high-To）. These materials carry layered square lattices with each layer being formed by vertex-shared...We suggest a new family of Co[Ni-based materials that may host unconventional high temperature superconductivity （high-To）. These materials carry layered square lattices with each layer being formed by vertex-shared transition metal tetrahedra cation-anion complexes. The electronic physics in these materials is determined by the two dimensional layer and is fully attributed to the three near degenerated t2g d-orbitals close to a d7 filling configuration in the d-shell of CoJNi atoms. The electronic structure meets the necessary criteria for unconventional high Tc materials proposed recently by us to unify the two known high-Tc families, cuprates and iron-based superconductors. We predict that they host superconducting states with a d-wave pairing symmetry with Tc potentially higher than those of iron-based superconductors. These materials, if realized, can be a fertile new ground to study strongly correlated electronic Physics and provide decisive evidence for superconducting pairing mechanism.展开更多
In this article,we have studied a nonlinear time–space fractional longitudinal wave equation in the context of the conformable fractional derivative.Through the soliton ansatz method and a direct integration approach...In this article,we have studied a nonlinear time–space fractional longitudinal wave equation in the context of the conformable fractional derivative.Through the soliton ansatz method and a direct integration approach with the symmetry condition,new soliton and solitary wave solutions are derived.Furthermore,the existing conditions of these obtained solutions are also given in this text.These new results add to the existing literature.We believe that they can provide a new window into the understanding of this model.展开更多
For the （2＋1）-dimensional Broer–Kaup–Kupershmidt（BKK） system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the ...For the （2＋1）-dimensional Broer–Kaup–Kupershmidt（BKK） system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the BKK system in the sense of having a consistent Riccati expansion（CRE） is investigated. The interaction solutions between soliton and cnoidal periodic wave are explicitly studied.展开更多
Crescent waves often observed on the sea surface are unusual wave pattern induced by the instability of Stokes wave.The paper presents the experimental results of the wave field around a circular cylinder generated by...Crescent waves often observed on the sea surface are unusual wave pattern induced by the instability of Stokes wave.The paper presents the experimental results of the wave field around a circular cylinder generated by the diffraction of crescent wave in order to examine the difference of diffracted crescent waves from the commonly-used diffracted Stokes waves. The results show that with the existence of the cylinder, the crescent wave pattern can still get fully developed, and with the presence of this type of wave pattern, the symmetry breaking of the wave amplitude distribution occurs and there are extra wave components at the frequencies of 0.5 ω;, 1.5ω;and 2.5ω;（ω;is the frequency of Stokes waves） appearing in the wave amplitude spectrum.展开更多
基金The project supported by Scientific Research and of Education Department of Heilongjiang Province of China under Grant No. 11511008
文摘Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhomogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero- Degasperis-Focas equation.
文摘A new method is proposed to numerically simulate problems of trains passing by each other at the same speed, and is implemented in UDF language of commercial software Fluent. Because only a half of the computational domain is required and the dynamic mesh technique is avoided, the computational efficiency is greatly improved. A two-dimensional test case is used for validation, which shows that the flow field and the pressure wave during the train-passing events can be correctly calculated by this new method. This method can be easily extended to three-dimensional simulations, to deal with practical problems.
基金Project supported by the National Natural Science Foundation of China(Nos.11071159 and11301259)the Shanghai Key Projects(No.12510501700)+1 种基金the Scientific Research of College of Inner Mongolia(No.NJZZ14053)the Natural Science Foundation of Inner Mongolia(Nos.2013MS0105and 2014MS0114)
文摘A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such nonlinear wave equations admit richer classical and nonclassical symmetries, leading to the conservation laws and the reduction of the wave equations. Some exact solutions of the considered wave equations for particular cases are derived.
文摘Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.
基金supported by the National Natural Science Foundation of China(No.12375006).
文摘A(2+1)-dimensional modified KdV(2DmKdV)system is considered from several perspectives.Firstly,residue symmetry,a type of nonlocal symmetry,and the Bäcklund transformation are obtained via the truncated Painlevéexpansion method.Subsequently,the residue symmetry is localized to a Lie point symmetry of a prolonged system,from which the finite transformation group is derived.Secondly,the integrability of the 2DmKdV system is examined under the sense of consistent tanh expansion solvability.Simultaneously,explicit soliton-cnoidal wave solutions are provided.Finally,abundant patterns of soliton molecules are presented by imposing the velocity resonance condition on the multiple-soliton solution.
基金Project supported by the National Key R&D Program of China(Grant No.2022YFA1204100)the National Natural Science Foundation of China(Grant No.62488201)+1 种基金the Chinese Academy of Sciences(Grant Nos.XDB33030000,ZDBS-SSW-WHC001,YSBR-003,and YSBR-053)Innovation Program of Quantum Science and Technology(Grant No.2021ZD0302700)。
文摘The kagome superconductor CsV_(3)Sb_(5) has attracted widespread attention due to its rich correlated electron states including superconductivity, charge density wave(CDW), nematicity, and pair density wave. Notably, the modulation of the intertwined electronic orders by the chemical doping is significant to illuminate the cooperation/competition between multiple phases in kagome superconductors. In this study, we have synthesized a series of tantalum-substituted Cs(V_(1-x)Ta_(x))_(3)Sb_(5) by a modified self-flux method. Electrical transport measurements reveal that CDW is suppressed gradually and becomes undetectable as the doping content of x is over 0.07. Concurrently, the superconductivity is enhanced monotonically from T_(c) ~ 2.8 K at x = 0 to 5.2 K at x = 0.12. Intriguingly, in the absence of CDW, Cs(V_(1-x)Ta_(x))_(3)Sb_(5)(x = 0.12) crystals exhibit a pronounced two-fold symmetry of the in-plane angular-dependent magnetoresistance(AMR) in the superconducting state, indicating the anisotropic superconducting properties in the Cs(V_(1-x)Ta_(x))_(3)Sb_(5). Our findings demonstrate that Cs(V_(1-x)Ta_(x))_(3)Sb_(5) with the non-trivial band topology is an excellent platform to explore the superconductivity mechanism and intertwined electronic orders in quantum materials.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11405103,11571008,51679132,11601321,and 11526137
文摘Applying the consistent Riccati expansion method, the extended(2+1)-dimensional shallow water wave equation is proved consistent Riccati solvable and the exact interaction solutions including soliton-cnoidal wave solutions,solitoff-typed solutions are obtained. With the help of the truncated Painlev′e expansion, the corresponding nonlocal symmetry is also given, and furthermore, the nonlocal symmetry is localized by prolonging the related enlarged system.
基金supported by the National Natural Science Foundation of China(Grant Nos.91852101,91952301 and 52179081).
文摘As a controllable alternative to cavitation collapse-induced shock waves,numerous cavitation studies on laser-induced breakdown have been carried out in hydromechanics.When the laser focusing region is not spherical,the shock waves caused by laser breakdown also exhibit non-spherical symmetry propagation.Recently,some researchers have proposed the linear superposition theory based on the far field measurement data to explain this asymmetry,assuming that it is essentially the linear superposition of multiple wave fronts caused by multiple points of laser-induced breakdown that leads to the asymmetric propagation of shock waves.In this study,measurements of shock wave propagation processes with different breakdown energies are carried out based on a nanosecond resolution photogrammetry system,and the propagation velocities of shock waves in different directions are directly measured using a double exposure technique on a single frame.In the experiment,the velocity of the shock wave at the beginning of the breakdown was measured up to nearly 4000 m/s.The early shock wave front was ellipsoidal,and the propagation velocity in the laser incident direction was generally slower than that in the perpendicular direction,decaying to the speed of sound in water within 1000 ns after the breakdown,and the wave front gradually approached to a circle.The variability of the shock wave front pressure ratio in the laser propagation direction and the vertical direction implies that the linear superposition theory applicable to the far field is not applicable to the near field.There may be more complex mechanism for the near-field shock wave propagation process.
基金Project supported by the Global Change Research Program of China(Grant No.2015CB953904)the National Natural Science Foundation of China(Grant Nos.11275072 and 11435005)+2 种基金the Doctoral Program of Higher Education of China(Grant No.20120076110024)the Network Information Physics Calculation of Basic Research Innovation Research Group of China(Grant No.61321064)the Fund from Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things(Grant No.ZF1213)
文摘In this paper,the truncated Painlev′e analysis,nonlocal symmetry,Bcklund transformation of the（2＋1）-dimensional modified Bogoyavlenskii–Schiff equation are presented.Then the nonlocal symmetry is localized to the corresponding nonlocal group by the prolonged system.In addition,the（2＋1）-dimensional modified Bogoyavlenskii–Schiff is proved consistent Riccati expansion（CRE） solvable.As a result,the soliton–cnoidal wave interaction solutions of the equation are explicitly given,which are difficult to find by other traditional methods.Moreover figures are given out to show the properties of the explicit analytic interaction solutions.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11975156 and 12175148)。
文摘Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of the two equations are obtained. The CRE method is applied to the two equations to obtain new B?cklund transformations from which a type of interesting interaction solution between solitons and periodic waves is generated.
基金supported by the National Basic Research Program of China (973 Program) (2015CB921300)the National Natural Science Foundation of China (11334012)the Strategic Priority Research Program of Chinese Academy of Sciences (XDB07000000)
文摘We suggest a new family of Co[Ni-based materials that may host unconventional high temperature superconductivity （high-To）. These materials carry layered square lattices with each layer being formed by vertex-shared transition metal tetrahedra cation-anion complexes. The electronic physics in these materials is determined by the two dimensional layer and is fully attributed to the three near degenerated t2g d-orbitals close to a d7 filling configuration in the d-shell of CoJNi atoms. The electronic structure meets the necessary criteria for unconventional high Tc materials proposed recently by us to unify the two known high-Tc families, cuprates and iron-based superconductors. We predict that they host superconducting states with a d-wave pairing symmetry with Tc potentially higher than those of iron-based superconductors. These materials, if realized, can be a fertile new ground to study strongly correlated electronic Physics and provide decisive evidence for superconducting pairing mechanism.
基金supported by the Yue-Qi Scholar of the China University of Mining and Technology(No.102504180004)。
文摘In this article,we have studied a nonlinear time–space fractional longitudinal wave equation in the context of the conformable fractional derivative.Through the soliton ansatz method and a direct integration approach with the symmetry condition,new soliton and solitary wave solutions are derived.Furthermore,the existing conditions of these obtained solutions are also given in this text.These new results add to the existing literature.We believe that they can provide a new window into the understanding of this model.
基金Project supported by the Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ13A010014)the National Natural Science Foundation of China(Grant Nos.11326164,11401528,11435005,and 11375090)
文摘For the （2＋1）-dimensional Broer–Kaup–Kupershmidt（BKK） system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the BKK system in the sense of having a consistent Riccati expansion（CRE） is investigated. The interaction solutions between soliton and cnoidal periodic wave are explicitly studied.
基金financially supported by the National Natural Science Fundation of China(Grant No.51879237)the Research Start Fund of Zhejiang Ocean University(Grant No.11185010817)
文摘Crescent waves often observed on the sea surface are unusual wave pattern induced by the instability of Stokes wave.The paper presents the experimental results of the wave field around a circular cylinder generated by the diffraction of crescent wave in order to examine the difference of diffracted crescent waves from the commonly-used diffracted Stokes waves. The results show that with the existence of the cylinder, the crescent wave pattern can still get fully developed, and with the presence of this type of wave pattern, the symmetry breaking of the wave amplitude distribution occurs and there are extra wave components at the frequencies of 0.5 ω;, 1.5ω;and 2.5ω;（ω;is the frequency of Stokes waves） appearing in the wave amplitude spectrum.
