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

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

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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