Title

Embedded solitons: a new type of solitary wave

Authors

Authors

J. Yang; B. A. Malomed; D. J. Kaup;A. R. Champneys

Comments

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Abbreviated Journal Title

Math. Comput. Simul.

Keywords

embedded soliton; multi-humped; Bragg gratings; KORTEWEG-DEVRIES EQUATION; GAP SOLITONS; QUADRATIC NONLINEARITY; OPTICAL; FIBERS; 2ND-HARMONIC GENERATION; EVOLUTION-EQUATIONS; MEDIA; STABILITY; DISPERSION; RESONANCE; Computer Science, Interdisciplinary Applications; Computer Science, ; Software Engineering; Mathematics, Applied

Abstract

We describe a novel class of solitary waves in second-harmonic-generation models with competing quadratic and cubic nonlinearities. These solitary waves exist at a discrete set of values of the propagation constants, being embedded inside the continuous spectrum of the linear system ("embedded solitons", ES). They are found numerically and, in a reduced model, in an exact analytical form too. We prove analytically and verify by direct simulations that the fundamental (single-humped) ESs are linearly stable, but are subject to a weak nonlinear one-sided instability. In some cases, the nonlinear instability is so weak that ES is a virtually stable object. Multi-humped embedded solitons are found too, all being linearly (strongly) unstable. (C) 2001 Published by Elsevier Science B.V. on behalf of IMACS.

Journal Title

Mathematics and Computers in Simulation

Volume

56

Issue/Number

6

Publication Date

1-1-2001

Document Type

Article

Language

English

First Page

585

Last Page

600

WOS Identifier

WOS:000169779800008

ISSN

0378-4754

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