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
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 new conservation theorem of the nonholonomic systems is studied. The conserved quantity is onlyconstructed in terms of a general Lie group of transformation vector of the dynamical equations. Firstly, we establish t...A new conservation theorem of the nonholonomic systems is studied. The conserved quantity is onlyconstructed in terms of a general Lie group of transformation vector of the dynamical equations. Firstly, we establish thedynamical equations of the nonholonomic systems and the determining equations of Lie symmetry. Next, the theore mof non-Noether conserved quantity is deduced. Finally, we give an example to illustrate the application of the result.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 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
The linear variable separation approach is successfully extended to (1+1)-dimensional Korteweg-de Vries (KdV) type models related to Schrǒdinger system. Some significant types of solitons such as compacton, peakon, a...The linear variable separation approach is successfully extended to (1+1)-dimensional Korteweg-de Vries (KdV) type models related to Schrǒdinger system. Some significant types of solitons such as compacton, peakon, and loop solutions with periodic behavior are simultaneously derived from the (1+1)-dimensional soliton system by entrancing appropriate piecewise smooth functions and multivalued functions.展开更多
By means of a special Painlevé-Backlund transformation and a multilinear variable separation approach,an exact solution with arbitrary functions of the (2+1)-dimensional Boiti-Leon-Pempinelli system (BLP) is deri...By means of a special Painlevé-Backlund transformation and a multilinear variable separation approach,an exact solution with arbitrary functions of the (2+1)-dimensional Boiti-Leon-Pempinelli system (BLP) is derived.Based on the derived variable separation solution, we obtain some special soliton fission and fusion solutions for the higher dimensional BLP system.展开更多
By means of the standard truncated Painleve expansion and a special Backlund transformation, the higher dimensional coupled Burgers system (HDCB) is reduced to a linear equation, and an exact multisoliton excitation i...By means of the standard truncated Painleve expansion and a special Backlund 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 solitoffdromion, 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.
基金国家自然科学基金，the Science Research Foundation of the Education Bureau of Anhui Province of China
文摘A new conservation theorem of the nonholonomic systems is studied. The conserved quantity is onlyconstructed in terms of a general Lie group of transformation vector of the dynamical equations. Firstly, we establish thedynamical equations of the nonholonomic systems and the determining equations of Lie symmetry. Next, the theore mof non-Noether conserved quantity is deduced. Finally, we give an example to illustrate the application of the result.
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 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.
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 Schrǒdinger system. Some significant types of solitons such as compacton, peakon, and loop solutions with periodic behavior are simultaneously derived from the (1+1)-dimensional soliton system by entrancing appropriate piecewise 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 Painlevé-Backlund transformation and a multilinear variable separation approach,an exact solution with arbitrary functions of the (2+1)-dimensional Boiti-Leon-Pempinelli system (BLP) is derived.Based on the derived variable separation solution, we obtain some special soliton fission and fusion solutions for the higher dimensional BLP system.
文摘By means of the standard truncated Painleve expansion and a special Backlund 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 solitoffdromion, they are combined with some new types of localized structures, which are similar to classic particles with completely nonelastic behaviors.
