Embedded solitons: a new type of solitary wave

J. Yang, B.A. Malomed, D.J. Kaup and A.R. Champneys

Mathematics and Computers in Simulation (MATCOM), 2001, vol. 56, issue 6, 585-600

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.

Keywords: Embedded soliton; Multi-humped; Bragg gratings (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:56:y:2001:i:6:p:585-600

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