R. Grimshaw, D. Pelinovsky, E. Pelinovsky and A. Slunyaev

The generation of large-amplitude solitons from an initial disturbance in the extended Korteweg-de Vries equation

Chaos 12, 1070-1076 (2002)

Abstract:
The generation of large-amplitude solitary waves from a localised initial condition is studied in the framework of the extended Korteweg-de Vries equation, that is, the usual Korteweg-de Vries equation with an extra cubic nonlinear term is included, for the case when the coefficient of the cubic nonlinear term has an opposite polarity to that of the coefficient of the linear dispersive term. As this equation is integrable, the number and type of solitons formed can be determined from an appropriate AKNS system, which is here solved for various forms of the initial disturbance. In contrast to some earlier results, we show that the number and type of solitons formed depend not only on the integral properties of the initial disturbance such as its mass and momentum, but also on the disturbance shape.

Keywords:
EXTENDED KORTEWEG-DE VRIES EQUATION, SOLITON GENERATION, ABLOWITS-KAUP-NEWELL-SEGUR SPECTRAL PROBLEM, MIURA TRANSFORMATION