Analytical solutions to a generalized Drinfel'd-Sokolov equation related to DSSH and KdV6
Abbreviated Journal Title
Appl. Math. Comput.
Drinfel'd-Sokolov equation; Analytical solution; Nonlinear PDE; HOMOTOPY ANALYSIS METHOD; NONLINEAR DIFFERENTIAL-EQUATIONS; TANH METHOD; W-ALGEBRAS; PERIODIC-SOLUTIONS; WILSON EQUATION; WAVE-EQUATIONS; REDUCTION; OPERATORS; EVOLUTION; Mathematics, Applied
Analytical solutions to the generalized Drinfel'd-Sokolov (GDS) equations u(t) + alpha(1)uu(x) + beta(1)u(xxx) + gamma(v(delta))(x) = 0 and v(t) + alpha(2)uv(x) + beta(2)v(xxx) = 0 are obtained for various values of the model parameters. In particular, we provide perturbation solutions to illustrate the strong influence of the parameters beta(1) and beta(2) 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 delta = 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 alpha(1) = -alpha(2). The method of homotopy analysis is applied in order to obtain analytical solutions to the resulting equation for arbitrary alpha(1) and alpha(2). An error analysis of the obtained approximate analytical solutions is provided. (C) 2010 Elsevier Inc. All rights reserved.
Applied Mathematics and Computation
"Analytical solutions to a generalized Drinfel'd-Sokolov equation related to DSSH and KdV6" (2010). Faculty Bibliography 2010s. 850.