Embedded solitons: a new type of solitary wave

Citation data:

Mathematics and Computers in Simulation, ISSN: 0378-4754, Vol: 56, Issue: 6, Page: 585-600

Publication Year:
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Repository URL:
http://stars.library.ucf.edu/facultybib2000/3012; http://stars.library.ucf.edu/facultybib/5217
J. Yang; B. A. Malomed; D. J. Kaup; A. R. Champneys
Elsevier BV
Mathematics; Computer Science; 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
article description
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.