Title
Analytical Solutions To A Generalized Drinfel'D-Sokolov Equation Related To Dssh And Kdv6
Keywords
Analytical solution; Drinfel'd-Sokolov equation; Nonlinear PDE
Abstract
Analytical solutions to the generalized Drinfel'd-Sokolov (GDS) equationsut + α1 uux + β1 uxxx + γ (vδ)x = 0 and vt + α2 uvx + β2 vxxx = 0are obtained for various values of the model parameters. In particular, we provide perturbation solutions to illustrate the strong influence of the parameters β1 and β2 on the behavior of the solutions. We then consider a Miura-type transform which reduces the gDS equations into a sixth-order nonlinear differential equation under the assumption that δ = 1. Under such a transform the GDS reduces to the sixth-order Drinfel'd-Sokolov-Satsuma-Hirota (DSSH) equation (also known as KdV6) in the very special case α1 = -α2. The method of homotopy analysis is applied in order to obtain analytical solutions to the resulting equation for arbitrary α1 and α2. An error analysis of the obtained approximate analytical solutions is provided. © 2010 Elsevier Inc. All rights reserved.
Publication Date
7-15-2010
Publication Title
Applied Mathematics and Computation
Volume
216
Issue
10
Number of Pages
2783-2791
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1016/j.amc.2010.03.128
Copyright Status
Unknown
Socpus ID
77953229125 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/77953229125
STARS Citation
Sweet, Erik and Van Gorder, Robert A., "Analytical Solutions To A Generalized Drinfel'D-Sokolov Equation Related To Dssh And Kdv6" (2010). Scopus Export 2010-2014. 697.
https://stars.library.ucf.edu/scopus2010/697