Variable Separation Approach for the Sine-Gordon System

2004 ◽  
Vol 59 (10) ◽  
pp. 629-634 ◽  
Author(s):  
Xian-jing Lai ◽  
Jie-fang Zhang
Keyword(s):  
Solitary Waves ◽  
Periodic Waves ◽  
Variable Separation ◽  
Elastic Interactions ◽  
Localized Excitations ◽  
Variable Separation Approach

Using the B¨acklund transformation and a variable separation approach with some arbitrary functions, three new types of solutions of the sine-Gordon system have been obtained. The excitations are localized as well as non-localized. E.g. solitoffs, dromions, multidromions, lumps, breathers, instantons, multivalued solitary waves, doubly periodic waves, etc., can be constructed on the basis of selecting the arbitrary functions properly. Also the interaction properties for all the possible localized excitations are of interest. In this paper, we discuss two elastic interactions. - PACS Ref: 05.45.Yv, 02.30.Jr, 02.30.Ik.

Multi-Soliton Excitations and Chaotic Patterns for the (2+1)-Dimensional Breaking-Soliton System

2010 ◽  
Vol 65 (6-7) ◽  
pp. 477-482 ◽  
Author(s):  
Li-Chen Lü ◽  
Song-Hua Ma ◽  
Jian-Ping Fang
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Wave Solutions ◽  
Localized Excitations ◽  
Variable Separation Approach

Starting from a projective equation and a linear variable separation approach, some solitary wave solutions with arbitrary functions for the (2+1)-dimensional breaking soliton system are derived. Based on the derived solution and by selecting appropriate functions, some novel localized excitations such as multi-solitons and chaotic-solitons are investigated.

Application of the Improved Mapping Approach to Exact Solutions and Chaotic Patterns for a Nonlinear Equation

2014 ◽  
Vol 945-949 ◽  
pp. 2430-2434
Author(s):  
Yan Lei ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Nonlinear Equation ◽  
Exact Solutions ◽  
Variable Separation ◽  
Mapping Approach ◽  
Localized Excitations ◽  
Variable Separation Approach

Starting from an improved mapping approach and a linear variable separation approach, a series of exact solutions of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli system (BLMP) is derived. Based on the derived variable separated solution, we obtain some special localized excitations such as dromion, solitoff and chaotic patterns.

Localized Coherent Soliton Structures in a Generalized (2+1)-Dimensional Nonlinear Schrödinger System

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4407-4414 ◽  
Author(s):  
Chun-Long Zheng ◽  
Zheng-Mao Sheng
Keyword(s):  
Coherent Structures ◽  
Bäcklund Transformation ◽  
Variable Separation ◽  
Backlund Transformation ◽  
Nonlinear Schrödinger ◽  
Localized Structures ◽  
Nonlinear Schrödinger System ◽  
Localized Excitations ◽  
Schrödinger System ◽  
Variable Separation Approach

A variable separation approach is used to obtain localized coherent structures in a generalized (2+1)-dimensional nonlinear Schrödinger system. Applying a special Bäcklund transformation and introducing arbitrary functions of the seed solutions, the abundance of the localized structures of this system are derived. By selecting the arbitrary functions appropriately, some special types of localized excitations such as dromions, dromion lattice, peakons, breathers and instantons are constructed.

scholarly journals Novel Soliton Molecules and Wave Interactions for A (3+1)-Dimensional Nonlinear Evolutionary Equation

2021 ◽  
Author(s):  
Xiaoyan Tang ◽  
Chao Jie Cui ◽  
Zu feng Liang ◽  
Wei Ding
Keyword(s):  
Nonlinear Evolution ◽  
Evolutionary Equation ◽  
New Wave ◽  
Variable Separation ◽  
Wave Interactions ◽  
Elastic Interactions ◽  
Localized Excitations ◽  
Soliton Lattice ◽  
Wave Patterns ◽  
Nonlinear Evolutionary Equation

Abstract New wave excitations are revealed for a (3+1)-dimensional nonlinear evolution equation to enrich nonlinear wave patterns in nonlinear systems. Based on a new variable separation solution with two arbitrary variable separated functions obtained by means of the multilinear variable separation approach, localized excitations of N dromions, N x M lump lattice and N x M ring soliton lattice are explored. Interestingly, it is observed that soliton molecules can be composed of diverse "atoms" such as the dromions, lumps and ring solitons, respectively. Elastic interactions between solitons and soliton molecules are graphically demonstrated.

Folded Localized Excitations and Chaotic Patterns in a (2+1)-Dimensional Soliton System

2008 ◽  
Vol 63 (3-4) ◽  
pp. 121-126 ◽  
Author(s):  
Song-Hua Ma ◽  
Jian-Ping Fang ◽  
Chun-Long Zheng
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Localized Excitations ◽  
Dimensional Soliton ◽  
Variable Separation Approach

Starting from an improved mapping approach and a linear variable separation approach, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for the (2+1)-dimensional breaking soliton system are derived. Based on the derived solitary wave solution, we obtain some special folded localized excitations and chaotic patterns.

scholarly journals Fusion and Annihilation of Solitary Waves for a (2+1)-Dimensional Nonlinear System

2010 ◽  
Vol 65 (12) ◽  
pp. 1151-1155 ◽  
Author(s):  
Ji-Ye Qiang ◽  
Song-Hua Ma ◽  
Qing-Bao Ren ◽  
Shao-Hua Wang
Keyword(s):  
Nonlinear System ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Wave Solutions ◽  
Localized Excitations

In this paper, a new projective equation is used to obtain the variable separation solutions with two arbitrary functions of the (2+1)-dimensional Broek-Kaup system (BKK). Based on the derived solitary wave solutions and by selecting appropriate functions, some novel localized excitations such as fusion and annihilation of solitary waves are investigated.

New Mapping Solutions and Line Soliton Excitations in a (1+1)-Dimensional Dispersive Long-Water Wave System

2013 ◽  
Vol 432 ◽  
pp. 117-121
Author(s):  
Ying Shi ◽  
Bing Ke Wang ◽  
Song Hua Ma
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Wave System ◽  
Variable Separation ◽  
New Family ◽  
Localized Excitations ◽  
Variable Separation Approach ◽  
Line Soliton

With the help of the symbolic computation system Maple and the mapping approach and a linear variable separation approach, a new family of exact solutions of the (1+1)-dimensional dispersive long-water wave system (DLWW) is derived. Based on the derived solitary wave solution, some novel localized excitations are investigated.

Compacton and Foldon Excitations in the Generalized (2+1)-dimensional Nizhnik-Novikov-Veselov Equation

2004 ◽  
Vol 59 (4-5) ◽  
pp. 250-256 ◽  
Author(s):  
Wen-Hua Huang ◽  
Jie-Fang Zhang ◽  
Wei-Gang Qiu
Keyword(s):  
Variable Separation ◽  
Localized Excitations ◽  
Variable Separation Approach ◽  
03.65 Ge

Using the variable separation approach, abundant localized coherent solutions are obtained for the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov (GNNV) equation. Two special types of localized excitations, compactons and foldons, are discussed. The behavior of the interactions for three-compacton solutions and two foldon solutions are investigated, and many interesting interaction properties are revealed. - PACS number: 02.30.Jr, 03.40.Kf, 03.65.Ge,05.45.Yv,03.65.-w

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