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
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 the use of the extended homogenous balance method,the B(?)cklund transformation for a (2+1)- dimensional integrable model,the(2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation,is obtained,and then the NNV equ...By the use of the extended homogenous balance method,the B(?)cklund transformation for a (2+1)- dimensional integrable model,the(2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation,is obtained,and then the NNV equation is transformed into three equations of linear,bilinear,and tri-linear forms,respectively.From the above three equations,a rather general variable separation solution of the model is obtained.Three novel class localized structures of the model are founded by the entrance of two variable-separated arbitrary functions.展开更多
Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solut...Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.展开更多
Using the variable separation approach, many types of exact solutions of the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study th...Using the variable separation approach, many types of exact solutions of the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study the interaction between a line soliton and a y-periodic soliton.展开更多
Considering that the multi-valued (folded) localized excitations may appear in many (2+1)-dimensional soliton equations because some arbitrary functions can be included in the exact solutions, we use some special type...Considering that the multi-valued (folded) localized excitations may appear in many (2+1)-dimensional soliton equations because some arbitrary functions can be included in the exact solutions, we use some special types of muliti-valued functions to construct folded solitrary waves and foldons in the (2+1)-dimensional Broer-Kaup equation.These folded excitations are invesigated both analytically and graphically in an alternative way.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
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
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 the use of the extended homogenous balance method,the B(?)cklund transformation for a (2+1)- dimensional integrable model,the(2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation,is obtained,and then the NNV equation is transformed into three equations of linear,bilinear,and tri-linear forms,respectively.From the above three equations,a rather general variable separation solution of the model is obtained.Three novel class localized structures of the model are founded by the entrance of two variable-separated arbitrary functions.
文摘Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.
文摘Using the variable separation approach, many types of exact solutions of the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study the interaction between a line soliton and a y-periodic soliton.
文摘Considering that the multi-valued (folded) localized excitations may appear in many (2+1)-dimensional soliton equations because some arbitrary functions can be included in the exact solutions, we use some special types of muliti-valued functions to construct folded solitrary waves and foldons in the (2+1)-dimensional Broer-Kaup equation.These folded excitations are invesigated both analytically and graphically in an alternative way.
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.
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.
