Exact Solutions and Solitons with Fission and Fusion Properties for the Generalized Broer-Kaup System

2006 ◽  
Vol 61 (1-2) ◽  
pp. 16-22
Author(s):  
Chun-Long Zheng ◽  
Jian-Ping Fang
Keyword(s):  
Exact Solutions ◽  
Variable Separation ◽  
Soliton Fission ◽  
Dimensional Soliton ◽  
Variable Separation Approach ◽  
03.65 Ge

Starting from a Painlev´e-B¨acklund transformation and a linear variable separation approach, we obtain a quite general variable separation excitation to the generalized (2+1)-dimensional Broer-Kaup (GBK) system. Then based on the derived solution, we reveal soliton fission and fusion phenomena in the (2+1)-dimensional soliton system. - PACS numbers: 05.45.Yv, 03.65.Ge

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.

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.

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.

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

Interaction between a Line Soliton and a Y-Periodic Soliton in the (2+1)-dimensional Nizhnik-Novikov-Veselov Equation

2002 ◽  
Vol 57 (12) ◽  
pp. 948-954 ◽  
Author(s):  
Hang-yu Ruan ◽  
Yi-xin Chen
Keyword(s):  
Exact Solutions ◽  
Long Range ◽  
Resonant Interaction ◽  
The Other ◽  
Variable Separation ◽  
Range Interaction ◽  
Long Range Interaction ◽  
Singular Interactions ◽  
Variable Separation Approach ◽  
Line Soliton

A variable separation approach is used to obtain exact solutions of the Nizhnik-Novikov- Veselov equation. Some exact solutions of this model are analysed to study the interaction between a line soliton and a y-periodic soliton. The interactions are classified into several types according to the phase shifts due to the collision. There are two types of singular interactions: One is the resonant interaction that generates one line soliton, while the other is the extremely repulsive or long-range interaction where two solitons interchange infinitely apart. Detailed behaviors of interactions are illustrated both analytically and graphically.

Exact Solutions and Localized Excitations of Burgers System in (3+1) Dimensions

2011 ◽  
Vol 66 (6-7) ◽  
pp. 383-391 ◽  
Author(s):  
Chun-Long Zheng ◽  
Hai-Ping Zhu
Keyword(s):  
Linear System ◽  
Exact Solutions ◽  
The Novel ◽  
Variable Separation ◽  
Linear Superposition ◽  
Localized Excitations ◽  
New Type ◽  
Superposition Theorem ◽  
Burgers System

With the help of a Cole-Hopf transformation, the nonlinear Burgers system in (3+1) dimensions is reduced to a linear system. Then by means of the linear superposition theorem, a general variable separation solution to the Burgers system is obtained. Finally, based on the derived solution, a new type of localized structure, i.e., a solitonic bubble is revealed and some evolutional properties of the novel localized structure are briefly discussed

Localized Excitations in a Dispersive Long Water-Wave System via an Extended Projective Approach

2007 ◽  
Vol 62 (3-4) ◽  
pp. 140-146 ◽  
Author(s):  
Jin-Xi Fei ◽  
Chun-Long Zheng
Keyword(s):  
Coherent Structures ◽  
Water Wave ◽  
Wave System ◽  
Variable Separation ◽  
Localized Excitations ◽  
Complex Wave ◽  
New Type ◽  
03.65 Ge

By means of an extended projective approach, a new type of variable separation excitation with arbitrary functions of the (2+1)-dimensional dispersive long water-wave (DLW) system is derived. Based on the derived variable separation excitation, abundant localized coherent structures such as single-valued localized excitations, multiple-valued localized excitations and complex wave excitations are revealed by prescribing appropriate functions. - PACS numbers: 03.65.Ge, 05.45.Yv

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.

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