Embedded solitons: a new type of solitary wave
Abbreviated Journal Title
Math. Comput. Simul.
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
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.
Mathematics and Computers in Simulation
"Embedded solitons: a new type of solitary wave" (2001). Faculty Bibliography 2000s. 3012.