Elastic and Annihilation Solitons of the (3+1)-Dimensional Generalized Shallow WaterWave System

2013 ◽  
Vol 68 (5) ◽  
pp. 350-354 ◽  
Author(s):  
Song-Hua Ma ◽  
Jian-Ping Fang ◽  
Hong-Yu Wu
Keyword(s):  
Exact Solution ◽  
Solitary Wave ◽  
Shallow Water ◽  
Symbolic Computation ◽  
Wave Solution ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Separation Method ◽  
Variable Separation ◽  
Variable Separation Method

With the help of the symbolic computation system Maple, the mapping approach, and a linear variable separation method, a new exact solution of the (3+1)-dimensional generalized shallow water wave (GSWW) system is derived. Based on the obtained solitary wave solution, some novel soliton excitations are investigated.

Study of the Variable Separation Solutions and Chaotic Behaviors for the Extended (2+1)-Dimensional Shallow Water Wave System

2013 ◽  
Vol 329 ◽  
pp. 144-147
Author(s):  
Xiao Xin Zhu ◽  
Song Hua Ma ◽  
Qing Bao Ren
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Water Wave ◽  
Mapping Method ◽  
Separation Method ◽  
Wave System ◽  
Variable Separation ◽  
Wave Excitation ◽  
Shallow Water Wave ◽  
Variable Separation Method

With the mapping method and a variable separation method, a series of variable separation solutions to the extended (2+1)-dimensional shallow water wave (ESWW) system is derived. Based on the derived solitary wave excitation, some chaotic behaviors are investigated.

Study of the Solitoff Solution and Fractal Solution for the (2+1)-Dimensional Broek-Kaup System with Variable Coefficients

2014 ◽  
Vol 532 ◽  
pp. 356-361
Author(s):  
Wei Ting Zhu
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Expansion Method ◽  
Variable Coefficients ◽  
Variable Separation ◽  
New Family ◽  
Localized Excitations ◽  
Variable Separation Method

Starting from a (G'/G)-expansion method and a variable separation method, a new family of exact solutions of the (2+1)-dimensional Broek-Kaup system with variable coefficients(VCBK) is obtained. Based on the derived solitary wave solution, we obtain some special localized excitations such as solitoff solutions and fractal solutions.

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.

Variable Separation Solutions for the (2+1)-Dimensional General Ablowitz-Kaup-Newell-Segur Equation

2012 ◽  
Vol 268-270 ◽  
pp. 1186-1189
Author(s):  
Jun Lei ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Solitary Wave ◽  
Riccati Equation ◽  
Symbolic Computation ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Variable Separation ◽  
New Family ◽  
Localized Excitations ◽  
Variable Separation Approach ◽  
Line Soliton

With the help of the symbolic computation system Maple and the Riccati equation projective approach and a linear variable separation approach, a new family of the variable separation solutions of the (2+1)-dimensional general Ablowitz-Kaup-Newell-Segur(GAKNS) equation is derived. Based on the derived solitary wave solution, we obtain some line-soliton localized excitations.

Exact Solitary-wave Solutions for the General Fifth-order Shallow Water-wave Models

1999 ◽  
Vol 54 (3-4) ◽  
pp. 272-274
Author(s):  
Woo-Pyo Hong ◽  
Young-Dae Jung
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Symbolic Computation ◽  
Water Wave ◽  
Model Parameters ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Special Cases ◽  
Wave Models ◽  
Fifth Order

We perform a computerized symbolic computation to find some general solitonic solutions for the general fifth-order shal-low water-wave models. Applying the tanh-typed method, we have found certain new exact solitary wave solutions. The pre-viously published solutions turn out to be special cases with restricted model parameters.

Bell Waves and Kind Waves for a (1+1)-Dimensional Nonlinear Partial Differential Equation

2013 ◽  
Vol 273 ◽  
pp. 831-834
Author(s):  
Qing Bao Ren ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Solitary Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Nonlinear Partial Differential Equation ◽  
Variable Separation ◽  
New Family ◽  
Variable Separation Approach ◽  
Burgers System

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 Burgers system is derived. Based on the derived solitary wave solution, some novel bell wave and kind wave excitations are investigated.

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.

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.

Understanding Peakons, Periodic Peakons and Compactons via a Shallow Water Wave Equation

2016 ◽  
Vol 26 (12) ◽  
pp. 1650207 ◽  
Author(s):  
Jibin Li ◽  
Wenjing Zhu ◽  
Guanrong Chen
Keyword(s):  
Shallow Water ◽  
Traveling Wave ◽  
Wave Solution ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Shallow Water Equation ◽  
Wave Model ◽  
Periodic Wave Solution ◽  
Wave System ◽  
Shallow Water Wave

In this paper, a shallow water wave model is used to introduce the concepts of peakon, periodic peakon and compacton. Traveling wave solutions of the shallow water equation are presented. The corresponding traveling wave system is a singular planar dynamical system with one singular straight line. By using the method of dynamical systems, bifurcation diagrams and explicit exact parametric representations of the solutions are given, including solitary wave solution, periodic wave solution, peakon solution, periodic peakon solution and compacton solution under different parameter conditions.

Study of the New Exact Solutions of a (3+1)-Dimensional Nonlinear Evolution Equation

2012 ◽  
Vol 268-270 ◽  
pp. 1182-1185
Author(s):  
Ma Biao Zhang
Keyword(s):  
Nonlinear Evolution Equation ◽  
Water Wave ◽  
Nonlinear Evolution ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Variable Separation Method

By the symbolic computation system Maple and the Riccati mapping approach and a variable separation method, some new variable separation solutions ( including solitory wave solutions and periodic wave solutions ) of the (3+1)-dimensional generalized shallow water wave (3DWW) system are derived. Based on the derived solitary wave solution, some novel solitoff solutions are investigated.

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