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.

New Exact Solutions for Two Nonlinear Equations

2006 ◽  
Vol 61 (1-2) ◽  
pp. 1-6 ◽  
Author(s):  
Zonghang Yang
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Exact Solutions ◽  
Water Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
New Exact Solutions ◽  
Complex Phenomena ◽  
Sivashinsky Equation

Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of science, for example the Korteweg-de Vries-Kuramoto-Sivashinsky equation (KdV-KS equation) and the Ablowitz-Kaup-Newell-Segur shallow water wave equation (AKNS-SWW equation). To our knowledge the exact solutions for the first equation were still not obtained and the obtained exact solutions for the second were just N-soliton solutions. In this paper we present kinds of new exact solutions by using the extended tanh-function method.

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

scholarly journals Symmetry Reduction, Exact Solutions, and Conservation Laws of the ZK-BBM Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Wenbin Zhang ◽  
Jiangbo Zhou ◽  
Sunil Kumar
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Invariant Solution ◽  
Lie Symmetry ◽  
Similarity Reduction ◽  
Group Invariant ◽  
New Exact Solutions ◽  
Reduction Group ◽  
The Given ◽  
Bbm Equation

Employing the classical Lie method, we obtain the symmetries of the ZK-BBM equation. Applying the given Lie symmetry, we obtain the similarity reduction, group invariant solution, and new exact solutions. We also obtain the conservation laws of ZK-BBM equation of the corresponding Lie symmetry.

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.

scholarly journals Symmetry reduction a promising method for heat conduction equations

2019 ◽  
Vol 23 (4) ◽  
pp. 2219-2227
Author(s):  
Yi Tian
Keyword(s):  
Heat Conduction ◽  
Exact Solutions ◽  
Wave Equations ◽  
Reduction Method ◽  
Variational Iteration Method ◽  
Mathematical Tool ◽  
Approximate Methods ◽  
Similarity Reduction ◽  
Homotopy Perturbation ◽  
Powerful Mathematical Tool

Though there are many approximate methods, e. g., the variational iteration method and the homotopy perturbation, for non-linear heat conduction equations, exact solutions are needed in optimizing the heat problems. Here we show that the Lie symmetry and the similarity reduction provide a powerful mathematical tool to searching for the needed exact solutions. Lie algorithm is used to obtain the symmetry of the heat conduction equations and wave equations, then the studied equations are reduced by the similarity reduction method.

scholarly journals New exact solutions of a generalized shallow water wave equation

2010 ◽  
Vol 82 (2) ◽  
pp. 025003 ◽  
Author(s):  
Bijan Bagchi ◽  
Supratim Das ◽  
Asish Ganguly
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Shallow Water Wave ◽  
New Exact Solutions
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