Title
Trigonometric And Hyperbolic Type Solutions To A Generalized Drinfel'D-Sokolov Equation
Keywords
Analytical solution; Exact solution; Generalized Drinfel'd-Sokolov equations; Nonlinear partial differential equation
Abstract
A class of trigonometric and hyperbolic type solutions to the generalized Drinfel'd-Sokolov (GDS) equationsut+α1uux+β1uxxx+γ(vδ)x= 0andvt+α2uvx+β2vxxx=0is obtained for the case in which α2 = 0, for various values of the other model parameters. The method of homotopy analysis is then applied to obtain local analytical solutions for nonzero values of the parameter α2, in effect extending the exact solutions. We do not assume traveling wave solution forms for the analytical solutions; that is, we solve the generalized Drinfel'd-Sokolov equations as PDEs without resorting to transforming the system to ODEs. An error analysis of the obtained approximate local analytical solutions is provided. Then, we outline a general framework by which one many construct solutions in either sine/cosine or sinh/cosh basis. We provide the general perturbation expansion via homotopy analysis, and we also discuss a method of selecting the convergence control parameter so as to minimize residual errors. Travelling solutions with time-dependent amplitude are then discussed. © 2010 Elsevier Inc. All rights reserved.
Publication Date
12-15-2010
Publication Title
Applied Mathematics and Computation
Volume
217
Issue
8
Number of Pages
4147-4166
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1016/j.amc.2010.09.064
Copyright Status
Unknown
Socpus ID
78149388322 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/78149388322
STARS Citation
Sweet, Erik and Van Gorder, Robert A., "Trigonometric And Hyperbolic Type Solutions To A Generalized Drinfel'D-Sokolov Equation" (2010). Scopus Export 2010-2014. 108.
https://stars.library.ucf.edu/scopus2010/108