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.

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.

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 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.

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.

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 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.

Study of the New Solitory Wave Solutions and Periodic Wave Solutions of a Two-Dimensional Modified KdV Equation

2013 ◽  
Vol 432 ◽  
pp. 122-126
Author(s):  
Mei Ling Gu ◽  
Zhi Hua Zhu ◽  
Song Hua Ma
Keyword(s):  
Kdv Equation ◽  
Periodic Wave ◽  
Mkdv Equation ◽  
Separation Method ◽  
Two Dimensional ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Modified Kdv Equation ◽  
Variable Separation Method

With the help of the Riccati mapping approach and the variable separation method, some new solitory wave solutions and periodic wave solutions of the two-dimensional modified KdV(MKdV) equation are derived.

The Periodic Wave Solutions for Two Nonlinear Evolution Equations

2003 ◽  
Vol 40 (2) ◽  
pp. 129-132 ◽  
Author(s):  
Zhang Jin-Liang ◽  
Wang Ming-Liang ◽  
Cheng Dong-Ming ◽  
Fang Zong-De
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Periodic Wave ◽  
Nonlinear Evolution Equations ◽  
Periodic Wave Solutions ◽  
Wave Solutions
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