Title

Exponential-Type Solutions To A Generalized Drinfel'D-Sokolov Equation

Abstract

Exact exponential-type solutions to the generalized Drinfel'd-Sokolov (GDS) equations ut + α1uux + β1 uxxx + γ (υδ) x =0 and υt + α2u υx + β2υxxx =0 are obtained for the case in which α2 = 0, for various values of the other model parameters. A modification of the homotopy analysis method is then applied to obtain analytical solutions for nonzero values of the parameter α2, in effect extending the exact solutions. In our modification of the standard method, we employ a nonlinear auxiliary operator. In contrast to most standard perturbation methods, in which a nonlinear problem is reduced to 'infinitely many' linear problems, here we reduce a hard nonlinear problem to 'infinitely many' easier nonlinear problems. Indeed, we also provide a solution using a linear auxiliary operator and show that the convergence of obtained solutions is improved (in the sense that fewer terms are required for the approximate solutions to obtain a desired accuracy) when using the auxiliary nonlinear operator, in some cases. An error analysis of the obtained approximate analytical solutions is provided. © 2010 The Royal Swedish Academy of Sciences.

Publication Date

9-1-2010

Publication Title

Physica Scripta

Volume

82

Issue

3

Number of Pages

-

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1088/0031-8949/82/03/035006

Socpus ID

78149367511 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/78149367511

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