Pii: S0378-4754(01)00327-5
نویسنده
چکیده
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. © 2001 Published by Elsevier Science B.V. on behalf of IMACS.
منابع مشابه
Pii: S0378-4754(01)00382-2
Noise-induced absolute instability is demonstrated in computer experiments with a one-dimensional reaction– diffusion system. This phenomenon may occur in spatially extended flow systems of different nature, when the parameters are chosen close to the point of transition from convective to absolute instability. © 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.
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