The Kawahara and modified Kawahara equations are fifth-order KdV type equations and have been derived to model many physical phenomena such as gravitycapillary waves and magneto-sound propagation in plasmas. This paper establishes the local well-posedness of the initial-value problem for Kawahara equation in H(R) with s > − 4 and the local well-posedness for the modified Kawahara equation in H(...

This paper extends the dual-Petrov-Galerkin method proposed by Shen [16] and further developed by Yuan, Shen and Wu [23] to several integrable and non-integrable fifth-order KdV type equations. These fifth-order equations arise in modeling different wave phenomena and involve various nonlinear terms. The method is implemented to compute the solitary wave solutions of these equations and the num...

In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional fifth-order KdV equation. A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed. In the sense of point symmetry, all of the vector fields and the symmetry reductions of the fractional fifth-order KdV equation are obtained. At last,...

We have derived solitary wave solutions of generalized KdV-type equations of fifth order in terms of certain hyperbolic functions and investigated their stability. It has been found that the introduction of more dispersive effects increases the stability range. 2000 Mathematics Subject Classification. 35Q53.

The interaction of solitary waves on shallow water is examined to fourth order. At first order the interaction is governed by the Korteweg–de Vries (KdV) equation, and it is shown that the unidirectional assumption, of right-moving waves only, is incompatible with mass conservation at third order. To resolve this, a mass conserving system of KdV equations, involving both rightand left-moving wa...

The adiabatic parameter dynamics of solitons, due to fifth order KdV-type equations with power law nonlinearity, is obtained with the aid of soliton perturbation theory. In addition, the small change in the velocity of the soliton, in the presence of perturbation terms, is also determined in this work. c © 2007 Elsevier Ltd. All rights reserved.