Volume no :48, Issue no: 1, November (2017)

Journal of Mathematical Sciences: Advances and Applications

NUMERICAL AND ASYMPTOTIC DESCRIPTION OF SOLITONS FOR GKdV EQUATIONS WITH NONHOMOGENEOUS NONLINEARITIES

Author's: J. Noyola Rodriguez and G. Omel’yanov
Pages: [27] - [46]
Received Date: November 18, 2017
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121891

Abstract

We consider a family of generalized KdV equations with a small dispersion and -nonlinearity We present sufficient conditions for under which a soliton type solution exists and, moreover, pairs of solitary waves collide preserving in an asymptotic sense the KdV-type scenario of interaction. Furthermore, we create a finite difference scheme to simulate the solution of the Cauchy problem and present some numerical results for the interaction problem.

Keywords

GKDV equation, solitons, interaction, numerical simulation, finite differences scheme.