scholarly journals Sine-Function Method In The Soliton Solution Of Nonlinear Partial Differential Equations

2013 ◽  
Vol 32 ◽  
pp. 55-60 ◽  
Author(s):  
M Abdur Rab ◽  
Jasmin Akhter
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solution ◽  
Sine Function ◽  
Partial Differential ◽  
Regularized Long Wave Equation ◽  
Different Types

In this paper we establish a traveling wave solution for nonlinear partial differential equations using sine-function method. The method is used to obtain the exact solutions for three different types of nonlinear partial differential equations like general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation(GKDV) which are the important soliton equations DOI: http://dx.doi.org/10.3329/ganit.v32i0.13647 GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 32 (2012) 55-60

Uniform progressing wave solutions of the wave equation

1971 ◽  
Vol 70 (3) ◽  
pp. 455-465
Author(s):  
Erich Zauderer
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Standard Form ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Wave Solutions ◽  
Different Types ◽  
Uniform Expansions

The solution of problems involving the propagation of discontinuities and other singularities for hyperbolic partial differential equations by means of progressing wave expansions is discussed in the book by Courant(l). He also refers to the work of Hadamard, Friedlander, Ludwig and others on this subject. More recently, Ludwig (2), Lewis(3) and others have considered 'uniform' progressing wave expansions for various problems. These expansions are valid in regions where the standard expansions are not suitable and they can be re-expanded in the standard form outside these regions. Examples of such regions are given by envelopes of bicharacteristic curves or, equivalently, caustics and by shadow boundaries such as occur in diffraction problems. In each of these regions, which we term 'transition regions' different types of uniform expansions are required.

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