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.

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 Time Evolution of Folded (2+1)-Dimensional Solitary Waves

2009 ◽  
Vol 64 (5-6) ◽  
pp. 309-314 ◽  
Author(s):  
Song-Hua Ma ◽  
Yi-Pin Lu ◽  
Jian-Ping Fang ◽  
Zhi-Jie Lv
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Water Wave ◽  
Periodic Wave ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Variable Separation Approach

Abstract With an extended mapping approach and a linear variable separation approach, a series of solutions (including theWeierstrass elliptic function solutions, solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave system (MDWW) is derived. Based on the derived solutions and using some multi-valued functions, we find a few new folded solitary wave excitations.

Study of the Exact Solutions and Chaotic Behaviors in a (2+1)-Dimensional Nonlinear System

2013 ◽  
Vol 340 ◽  
pp. 755-759
Author(s):  
Song Hua Ma
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Variable Separation Approach

With the help of the symbolic computation system Maple and the (G'/G)-expansion approach and a special variable separation approach, a series of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave (MDWW) system is derived. Based on the derived solitary wave solution, some novel domino solutions and chaotic patterns are investigated.

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 Exact Solutions and Complex Wave Excitations for the (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov System

2008 ◽  
Vol 63 (10-11) ◽  
pp. 641-645
Author(s):  
Jiang-Bo Li ◽  
Chun-Long Zheng ◽  
Song-Hua Ma
Keyword(s):  
Solitary Wave ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Complex Wave ◽  
Special Complex ◽  
Variable Separation Approach

Starting from an improved mapping approach and a linear variable separation approach, new families of variable separated solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for the (2+1)-dimensional asymmetric Nizhnik- Novikov-Veselov (ANNV) system are derived. Based on the derived solutions, we obtain some special complex wave excitations.

Evolution Properties of the y-Periodic Solitons for the (2+1)-Dimensional Boiti-Leon-Pempinelli System

2007 ◽  
Vol 62 (1-2) ◽  
pp. 1-7
Author(s):  
Xiao-Fei Wu ◽  
Zheng-Yi Ma ◽  
Jia-Min Zhu
Keyword(s):  
Solitary Wave ◽  
Trigonometric Function ◽  
Explicit Solutions ◽  
Equation Approach ◽  
Solitary Wave Solutions ◽  
Weierstrass Function ◽  
Localized Structures ◽  
Wave Solutions ◽  
Localized Excitations ◽  
Trigonometric Function Solutions

With the help of the symbolic computation system Maple and an expanded projective Riccati equation approach, we obtain some new rational explicit solutions with three arbitrary functions for the (2+1)-dimensional Boiti-Leon-Pempinelli system, including Weierstrass function solutions, solitary wave solutions and trigonometric function solutions. From these, several y-periodic soliton localized excitations are constructed and some evolution properties of these novel y-periodic localized structures are discussed.

Solitary Wave and Periodic Wave Solutions and Chaotic Behaviors in a (2+1)-Dimensional Nonlinear System

2014 ◽  
Vol 532 ◽  
pp. 346-350
Author(s):  
Xiao Xin Zhu ◽  
Song Hua Ma ◽  
Qing Bao Ren
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Mapping Method ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Variable Separation Method

With the help of the symbolic computation system Maple and an improved mapping method and a variable separation method, a series of new exact solutions (including solitary wave solutions and periodic wave solutions) to the (2+1)-dimensional general Nizhnik-Novikov-Veselov (GNNV) system is derived. Based on the derived solitary wave solution, we obtain some chaotic patterns.

Investigation of (G'/G)-Expansion Method and Exact Solutions for the (2+1)-Dimensional Calogero-Bogoyavlenskii-Schiff System

2013 ◽  
Vol 432 ◽  
pp. 235-239
Author(s):  
Gen Hai Xu ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
New Family ◽  
Wave Solutions ◽  
Variable Separation Method

With the help of the symbolic computation system Maple and the (G'/G)-expansion method and a linear variable separation method, a new family of exact solutions (including solitary wave solutions,periodic wave solutions and rational function solutions) of the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff system (2DCBS) is derived.

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.

Solitary Wave Solutions, Periodic Wave Solutions and Folded Localized Excitations for the Dissipative Zabolotskaya-Khokhlov System

2014 ◽  
Vol 599-601 ◽  
pp. 1712-1715
Author(s):  
Qing Bao Ren ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Solitary Wave Solution ◽  
Nonlinear Partial Differential Equations ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Mapping Approach ◽  
Localized Excitations

The mapping approach is a powerful tool to looking for the exact solutions for nonlinear partial differential equations. In this paper, using an improved mapping approach, a series of exact solutions (including solitary wave solutions and periodic wave solutions) of the (2+1)-dimensional dissipative Zabolotskaya Khokhlov (DZK) system is derived. Based on the derived solitary wave solution, we obtain some folded localized excitations of the DZK system.

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