Conditional Similarity Reduction Method and Complex Wave Excitations for a High-Dimensional Nonlinear System

2015 ◽  
Vol 70 (9) ◽  
pp. 739-744
Author(s):  
Fu-Zhong Lin ◽  
Song-Hua Ma
Keyword(s):  
Nonlinear System ◽  
Water Wave ◽  
Reduction Method ◽  
Solitary Wave Solution ◽  
High Dimensional ◽  
Similarity Reduction ◽  
New Family ◽  
Wave Solutions ◽  
Complex Wave ◽  
Novel Complex

AbstractWith the help of the conditional similarity reduction method, a new family of complex wave solutions with q=lx + my + kt + Γ(x, y, t) for the (2+1)-dimensional modified dispersive water-wave (MDWW) system are obtained. Based on the derived solitary wave solution, some novel complex wave localised excitations are investigated.

New Exact Solutions and Localized Excitations in a (2+1)-Dimensional Soliton System

2009 ◽  
Vol 64 (1-2) ◽  
pp. 37-43
Author(s):  
Song-Hua Ma ◽  
Jian-Ping Fang
Keyword(s):  
Exact Solutions ◽  
Water Wave ◽  
Reduction Method ◽  
Wave System ◽  
Similarity Reduction ◽  
New Exact Solutions ◽  
Localized Excitations ◽  
Reduction Equation ◽  
Dimensional Soliton

Starting from a special conditional similarity reduction method, we obtain the reduction equation of the (2+1)-dimensional dispersive long-water wave system. Based on the reduction equation, some new exact solutions and abundant localized excitations are obtained.

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.

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.

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.

scholarly journals Novel Complex Wave Solutions of the (2+1)-Dimensional Hyperbolic Nonlinear Schrödinger Equation

2020 ◽  
Vol 4 (3) ◽  
pp. 41 ◽  
Author(s):  
Hulya Durur ◽  
Esin Ilhan ◽  
Hasan Bulut
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Complex Wave ◽  
Novel Complex ◽  
Parameter Values

This manuscript focuses on the application of the (m+1/G′)-expansion method to the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation. With the help of projected method, the periodic and singular complex wave solutions to the considered model are derived. Various figures such as 3D and 2D surfaces with the selecting the suitable of parameter values are plotted.

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