Perturbation-induced perestroika of a nonlinear-Schrödinger breather

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Abstract

The evolution of an N-soliton state (breather) is considered in the nonlinear Schrödinger equation with a sufficinetly arbitrary conservative perturbing term. Arguments are given in favor of a perestroika (rearrangement) of the breather into the exact one-soliton state via emission of radiation. For the two-soliton breather, it is demonstrated that an approximate kinematic analysis, based on the balance equation for the wave action and energy, makes it possible to find the amplitude of the one-soliton state as a function of the two initial amplitudes of the breather, provided one of them is sufficiently small compared to the other. The expression for the final amplitude proves to be very simple, and it is universal in the sense that it does not depend on a particular form of the conservative perturbation. As an example, nonlinear surface elastic modes in a crystal are considered. It is shown that N-soliton surface modes may undergo the emission-assisted prestroika into the exact one-soliton mode under the action of a nonlinear correction to the boundary condition at the surface.

Original languageEnglish
Pages (from-to)441-444
Number of pages4
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume154
Issue number9
DOIs
StatePublished - 22 Apr 1991
Externally publishedYes

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