Embedded solitons: a new type of solitary wave

    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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