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.

Complexiton and solitary wave solutions of the coupled nonlinear Maccari’s system using two integration schemes

2018 ◽  
Vol 32 (02) ◽  
pp. 1850014 ◽  
Author(s):  
Mustafa Inc ◽  
Aliyu Isa Aliyu ◽  
Abdullahi Yusuf ◽  
Dumitru Baleanu ◽  
Elif Nuray
Keyword(s):  
Numerical Simulation ◽  
Solitary Wave ◽  
Riccati Equation ◽  
Physical Meaning ◽  
Trigonometric Function ◽  
Solitary Wave Solutions ◽  
Integration Schemes ◽  
Wave Solutions ◽  
Trigonometric Function Solutions

In this paper, we consider a coupled nonlinear Maccari’s system (CNMS) which describes the motion of isolated waves localized in a small part of space. There are some integration tools that are adopted to retrieve the solitary wave solutions. They are the modified F-Expansion and the generalized projective Riccati equation methods. Topological, non-topological, complexiton, singular and trigonometric function solutions are derived. A comparison between the results in this paper and the well-known results in the literature is also given. The derived structures of the obtained solutions offer a rich platform to study the nonlinear CNMS. Numerical simulation of the obtained solutions are presented with interesting figures showing the physical meaning of the solutions.

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.

scholarly journals Cusped and Smooth Solitons for the Generalized Camassa-Holm Equation on the Nonzero Constant Pedestal

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Dong Li ◽  
Yongan Xie ◽  
Shengqiang Tang
Keyword(s):  
Solitary Wave ◽  
Numerical Simulations ◽  
Mathematical Analysis ◽  
Soliton Solutions ◽  
Explicit Solutions ◽  
Solitary Wave Solutions ◽  
Nonzero Constant ◽  
Wave Solutions ◽  
Holm Equation

We investigate the traveling solitary wave solutions of the generalized Camassa-Holm equationut - uxxt + 3u2ux=2uxuxx + uuxxxon the nonzero constant pedestallimξ→±∞⁡uξ=A. Our procedure shows that the generalized Camassa-Holm equation with nonzero constant boundary has cusped and smooth soliton solutions. Mathematical analysis and numerical simulations are provided for these traveling soliton solutions of the generalized Camassa-Holm equation. Some exact explicit solutions are obtained. We show some graphs to explain our these solutions.

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.

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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