Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broe...Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broer-Kaup system. From this expression, we investigate the interactions of localized coherent structures such as the multi-solitonic excitations and find the novel phenomenon that their interactions have non-elastic behavior because the fission/fusion may occur after the interaction of each localized coherent structure.展开更多
A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic w...A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.展开更多
With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the deri...With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.展开更多
In the previous Letter (Zheng C L and Zhang J F 2002 China.Phys.Lett.19 1399),a localized excitation of the generalized Ablowitz-Kaup-Newell Segur(GAKNS) system was obtained via the standard Painlevé truncated ex...In the previous Letter (Zheng C L and Zhang J F 2002 China.Phys.Lett.19 1399),a localized excitation of the generalized Ablowitz-Kaup-Newell Segur(GAKNS) system was obtained via the standard Painlevé truncated expansion and a special variable separation approach. In this work, starting from a new variable separation approach, a more general variable separation excitation of this system is derived. The abundance of the localized coherent soliton excitations like dromions, lumps,rings, peakons and oscillating soliton excitations can be constructed by introducing appropriate lower-dimensional soliton patterns. Meanwhile we discuss two kinds of interactions of solitons. One is the interaction between the travelling peakon type soliton excitations,which is not completely elastic. The other is the interaction between the travelling ring type soliton excitations, which is completely elastic.展开更多
A simple and direct method is applied to solving the (2+1)-dimensional perturbed Ablowitz–Kaup–Newell–Segur system (PAKNS). Starting from a special B?cklund transformation and the variable separation approach, we c...A simple and direct method is applied to solving the (2+1)-dimensional perturbed Ablowitz–Kaup–Newell–Segur system (PAKNS). Starting from a special B?cklund transformation and the variable separation approach, we convert the PAKNS system into the simple forms, which are four variable separation equations, then obtain a quite general solution. Some special localized coherent structures like fractal dromions and fractal lumps of this model are constructed by selecting some types of lower-dimensional fractal patterns.展开更多
Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained...Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained. In addition to the single-valued localized coherent soliron excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.展开更多
By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: is derived. Some types of the usual localized excitations such as dromions, lumps, ring...By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, fractal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.展开更多
In this work, an adaptation of the tanh/tan-method that is discussed usually in the nonlinear partial differential equations is presented to solve nonlinear polynomial differential-difference equations. As a concrete ...In this work, an adaptation of the tanh/tan-method that is discussed usually in the nonlinear partial differential equations is presented to solve nonlinear polynomial differential-difference equations. As a concrete example,several solitary wave and periodic wave solutions for the chain which is related to the relativistic Toda lattice are derived.Some systems of the differential-difference equations that can be solved using our approach are listed and a discussion is given in conclusion.展开更多
In the present paper, a simple and direct method was proposed to solve the (2+ 1)-dimensional long dispersive wave equations. A variable-dependent transformation was intorducedto convert the equations into the simpler...In the present paper, a simple and direct method was proposed to solve the (2+ 1)-dimensional long dispersive wave equations. A variable-dependent transformation was intorducedto convert the equations into the simpler forms, which are coupled and linear partial differentialequations, then obtain its general solution. Some special types of the localized excitations, suchas oscillating dromion, multi-solitoff, multi-dromion, multi-lump and multi-ring soliton solutionsare derived by selecting the arbitrary functions appropriately.展开更多
In this paper, the variable separation approach is used to obtain localized coherent structures of the (2+1)-dimensional generalized Davey-Stewarson equations: iqt + 1/2(qxx + qyy) + (R+ S)q = O, Rx=-σ/2|q|2y Sy = -...In this paper, the variable separation approach is used to obtain localized coherent structures of the (2+1)-dimensional generalized Davey-Stewarson equations: iqt + 1/2(qxx + qyy) + (R+ S)q = O, Rx=-σ/2|q|2y Sy = -σ/2|q|2/x.Applying a special Backlund transformation and introducing arbitrary functions of the seed solutions, an abundance of the localized structures of this model is derived. By selecting the arbitrary functions appropriately, some special typesof localized excitations such as dromions, dromion lattice, breathers, and instantons are constructed.展开更多
In this work, we reveal a novel phenomenon that the localized coherent structures of some (2+1)-dimensional physical models possess chaotic and fractal behaviors. To clarify these interesting phenomena, we take the (...In this work, we reveal a novel phenomenon that the localized coherent structures of some (2+1)-dimensional physical models possess chaotic and fractal behaviors. To clarify these interesting phenomena, we take the (2+l)-dimensional modified dispersive water-wave system as a concrete example. Starting from a variable separation approach,a general variable separation solution of this system is derived. Besides the stable located coherent soliton excitations like dromions, lumps, rings, peakons, and oscillating soliton excitations, some new excitations with chaotic and fractal behaviors are derived by introducing some types of lower dimensional chaotic and fractal patterns.展开更多
By means ora Painlevé-Backlund transformation and a multi-linear variable separation approach, abundant localized coherent excitations of the three-dimensional Broer-Kaup-Kupershmidt system with variable coeffici...By means ora Painlevé-Backlund transformation and a multi-linear variable separation approach, abundant localized coherent excitations of the three-dimensional Broer-Kaup-Kupershmidt system with variable coefficients are derived. There are possible phase shifts for the interactions of the three-dimensional novel localized structures discussed in this paper.展开更多
A novel phenomenon that the localized coherent structures of a (2+1)-dimensional physical model possess fractal behaviors is revealed. To clarify the interesting phenomenon, we take the (2+1)-dimensional Boiti-Leon Pe...A novel phenomenon that the localized coherent structures of a (2+1)-dimensional physical model possess fractal behaviors is revealed. To clarify the interesting phenomenon, we take the (2+1)-dimensional Boiti-Leon Pempinelli system as a concrete example. Starting from an extended homogeneous balance approach, a general solution of the system is derived. From which some special localized excitations with fractal behaviors are obtained by introducing some types of lower-dimensional fractal patterns.展开更多
The linear variable separation approach is successfully extended to(1+1)-dimensional Korteweg-de Vries (KdV) type models related to Schrodinger system. Somesignificant types of solitons such as compaction, peakon, and...The linear variable separation approach is successfully extended to(1+1)-dimensional Korteweg-de Vries (KdV) type models related to Schrodinger system. Somesignificant types of solitons such as compaction, peakon, and loop solutions with periodic behaviorare simultaneously derived from the (l+l)-dimensional soliton system by entrancing appropriatepiecewise smooth functions and multivalued functions.展开更多
By means of a special Painleve—Baecklund transformation and a multilinearvariable separation approach, an exact solution with arbitrary functions of the (2+1)-dimensionalBoiti-Leon-Pempinelli system (BLP) is derived....By means of a special Painleve—Baecklund transformation and a multilinearvariable separation approach, an exact solution with arbitrary functions of the (2+1)-dimensionalBoiti-Leon-Pempinelli system (BLP) is derived. Based on the derived variable separation solution, weobtain some special soliton fission and fusion solutions for the higher dimensional BLP system.展开更多
Using an extended projective method, a new type of variable separation solution with two arbitrary functions of the (2+1)-dimensional generalized Broer-Kaup system (GBK) is derived. Based on the derived variable separ...Using an extended projective method, a new type of variable separation solution with two arbitrary functions of the (2+1)-dimensional generalized Broer-Kaup system (GBK) is derived. Based on the derived variable separation solution, some special localized coherent soliton excitations with or without elastic behaviors such as dromions, peakons,and foldons etc. are revealed by selecting appropriate functions in this paper.展开更多
By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized co...By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakons, foldons, and previously revealed chaotic and fractal localized solutions, some new types of excitations — compacton and Jacobi periodic wave solutions are obtained by introducing appropriate lower dimensional piecewise smooth functions and Jacobi elliptic functions.展开更多
By means of the standard truncated Painlevé expansion and a special B?cklund transformation, the higher-dimensional coupled Burgers system (HDCB) is reduced to a linear equation, and an exact multisoliton excitat...By means of the standard truncated Painlevé expansion and a special B?cklund transformation, the higher-dimensional coupled Burgers system (HDCB) is reduced to a linear equation, and an exact multisoliton excitation is derived. The evolution properties of the multisoliton excitation are investigated and some novel features or interesting behaviors are revealed. The results show that after interactions for dromion-dromion, solitoff-solitoff, and solitoff-dromion, they are combined with some new types of localized structures, which are similar to classic particles with completely nonelastic behaviors.展开更多
文摘Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broer-Kaup system. From this expression, we investigate the interactions of localized coherent structures such as the multi-solitonic excitations and find the novel phenomenon that their interactions have non-elastic behavior because the fission/fusion may occur after the interaction of each localized coherent structure.
文摘A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.
文摘With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.
文摘In the previous Letter (Zheng C L and Zhang J F 2002 China.Phys.Lett.19 1399),a localized excitation of the generalized Ablowitz-Kaup-Newell Segur(GAKNS) system was obtained via the standard Painlevé truncated expansion and a special variable separation approach. In this work, starting from a new variable separation approach, a more general variable separation excitation of this system is derived. The abundance of the localized coherent soliton excitations like dromions, lumps,rings, peakons and oscillating soliton excitations can be constructed by introducing appropriate lower-dimensional soliton patterns. Meanwhile we discuss two kinds of interactions of solitons. One is the interaction between the travelling peakon type soliton excitations,which is not completely elastic. The other is the interaction between the travelling ring type soliton excitations, which is completely elastic.
文摘A simple and direct method is applied to solving the (2+1)-dimensional perturbed Ablowitz–Kaup–Newell–Segur system (PAKNS). Starting from a special B?cklund transformation and the variable separation approach, we convert the PAKNS system into the simple forms, which are four variable separation equations, then obtain a quite general solution. Some special localized coherent structures like fractal dromions and fractal lumps of this model are constructed by selecting some types of lower-dimensional fractal patterns.
文摘Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained. In addition to the single-valued localized coherent soliron excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.
文摘By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, fractal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.
文摘In this work, an adaptation of the tanh/tan-method that is discussed usually in the nonlinear partial differential equations is presented to solve nonlinear polynomial differential-difference equations. As a concrete example,several solitary wave and periodic wave solutions for the chain which is related to the relativistic Toda lattice are derived.Some systems of the differential-difference equations that can be solved using our approach are listed and a discussion is given in conclusion.
文摘In the present paper, a simple and direct method was proposed to solve the (2+ 1)-dimensional long dispersive wave equations. A variable-dependent transformation was intorducedto convert the equations into the simpler forms, which are coupled and linear partial differentialequations, then obtain its general solution. Some special types of the localized excitations, suchas oscillating dromion, multi-solitoff, multi-dromion, multi-lump and multi-ring soliton solutionsare derived by selecting the arbitrary functions appropriately.
文摘In this paper, the variable separation approach is used to obtain localized coherent structures of the (2+1)-dimensional generalized Davey-Stewarson equations: iqt + 1/2(qxx + qyy) + (R+ S)q = O, Rx=-σ/2|q|2y Sy = -σ/2|q|2/x.Applying a special Backlund transformation and introducing arbitrary functions of the seed solutions, an abundance of the localized structures of this model is derived. By selecting the arbitrary functions appropriately, some special typesof localized excitations such as dromions, dromion lattice, breathers, and instantons are constructed.
文摘In this work, we reveal a novel phenomenon that the localized coherent structures of some (2+1)-dimensional physical models possess chaotic and fractal behaviors. To clarify these interesting phenomena, we take the (2+l)-dimensional modified dispersive water-wave system as a concrete example. Starting from a variable separation approach,a general variable separation solution of this system is derived. Besides the stable located coherent soliton excitations like dromions, lumps, rings, peakons, and oscillating soliton excitations, some new excitations with chaotic and fractal behaviors are derived by introducing some types of lower dimensional chaotic and fractal patterns.
文摘By means ora Painlevé-Backlund transformation and a multi-linear variable separation approach, abundant localized coherent excitations of the three-dimensional Broer-Kaup-Kupershmidt system with variable coefficients are derived. There are possible phase shifts for the interactions of the three-dimensional novel localized structures discussed in this paper.
文摘A novel phenomenon that the localized coherent structures of a (2+1)-dimensional physical model possess fractal behaviors is revealed. To clarify the interesting phenomenon, we take the (2+1)-dimensional Boiti-Leon Pempinelli system as a concrete example. Starting from an extended homogeneous balance approach, a general solution of the system is derived. From which some special localized excitations with fractal behaviors are obtained by introducing some types of lower-dimensional fractal patterns.
基金The project supported by National Natural Science Foundation of China under Grant No. 10172056, and the Natural Science Foundation of Zhejiang Province of China under Grant No. Y604106 and the Natural Science Foundation of Zhejiang Lishui University unde
文摘The linear variable separation approach is successfully extended to(1+1)-dimensional Korteweg-de Vries (KdV) type models related to Schrodinger system. Somesignificant types of solitons such as compaction, peakon, and loop solutions with periodic behaviorare simultaneously derived from the (l+l)-dimensional soliton system by entrancing appropriatepiecewise smooth functions and multivalued functions.
基金国家自然科学基金，the Scientific Research Fund of Educational Department of Zhejiang Province of China under，浙江省自然科学基金
文摘By means of a special Painleve—Baecklund transformation and a multilinearvariable separation approach, an exact solution with arbitrary functions of the (2+1)-dimensionalBoiti-Leon-Pempinelli system (BLP) is derived. Based on the derived variable separation solution, weobtain some special soliton fission and fusion solutions for the higher dimensional BLP system.
文摘Using an extended projective method, a new type of variable separation solution with two arbitrary functions of the (2+1)-dimensional generalized Broer-Kaup system (GBK) is derived. Based on the derived variable separation solution, some special localized coherent soliton excitations with or without elastic behaviors such as dromions, peakons,and foldons etc. are revealed by selecting appropriate functions in this paper.
基金The project supported by National Natural Science Foundation of China under Grant No.10172056+2 种基金the Natural Science Foundation of Zhengjiang Provincethe Foundation of Zhengjiang Lishui College under Grant Nos.KZ03009 and KZ03005
文摘By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakons, foldons, and previously revealed chaotic and fractal localized solutions, some new types of excitations — compacton and Jacobi periodic wave solutions are obtained by introducing appropriate lower dimensional piecewise smooth functions and Jacobi elliptic functions.
文摘By means of the standard truncated Painlevé expansion and a special B?cklund transformation, the higher-dimensional coupled Burgers system (HDCB) is reduced to a linear equation, and an exact multisoliton excitation is derived. The evolution properties of the multisoliton excitation are investigated and some novel features or interesting behaviors are revealed. The results show that after interactions for dromion-dromion, solitoff-solitoff, and solitoff-dromion, they are combined with some new types of localized structures, which are similar to classic particles with completely nonelastic behaviors.
