Artículo
Soliton stability criterion for generalized nonlinear Schrödinger equations
Autor/es | Quintero, Niurka R.
Mertens, Franz G. Bishop, Alan R. |
Departamento | Universidad de Sevilla. Departamento de Física Aplicada I |
Fecha de publicación | 2015 |
Fecha de depósito | 2015-08-24 |
Publicado en |
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Resumen | A stability criterion for solitons of the driven nonlinear Schrödinger equation (NLSE) has been conjectured. The criterion states that p′(v)<0 is a sufficient condition for instability, while p′(v)>0 is a necessary condition ... A stability criterion for solitons of the driven nonlinear Schrödinger equation (NLSE) has been conjectured. The criterion states that p′(v)<0 is a sufficient condition for instability, while p′(v)>0 is a necessary condition for stability; here, v is the soliton velocity and p=P/N, where P and N are the soliton momentum and norm, respectively. To date, the curve p(v) was calculated approximately by a collective coordinate theory, and the criterion was confirmed by simulations. The goal of this paper is to calculate p(v) exactly for several classes and cases of the generalized NLSE: a soliton moving in a real potential, in particular a time-dependent ramp potential, and a time-dependent confining quadratic potential, where the nonlinearity in the NLSE also has a time-dependent coefficient. Moreover, we investigate a logarithmic and a cubic NLSE with a time-independent quadratic potential well. In the latter case, there is a bisoliton solution that consists of two solitons with asymmetric shapes, forming a bound state in which the shapes and the separation distance oscillate. Finally, we consider a cubic NLSE with parametric driving. In all cases, the p(v) curve is calculated either analytically or numerically, and the stability criterion is confirmed. |
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