##
K.A. Gorshkov and D.E. Pelinovsky

#
Asymptotic theory of plane soliton self-focusing
in two-dimensional wave media

###
Physica D 85, 468-484 (1995)

**Abstract:**

An asymptotic method is developed to describe a long-term
evolution of unstable quasi-plane solitary waves in the
Kadomtsev-Petviashvili model for two-dimensional
wave media with positive dispersion. An approximate equation
is derived for the parameters of soliton transversal modulation
and a general solution of this equation is
found in an explicit form. It is shown that the development of
periodic soliton modulation, in an unstable region, leads to
saturation and formation of a two-dimensional
stationary wave. This process is accompanied by the radiation
of a small-amplitude plane soliton. In a stable region, an
amplitude of the modulation is permanently
decreasing due to radiation of quasi-harmonic wave packets.
The multiperiodic regime of plane soliton self-focusing is
also investigated.

**Keywords:**

EVOLUTION, INSTABILITY, TRANSITION, STABILITY, EQUATION, PLASMAS