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Soliton stability criterion for generalized nonlinear Schrödinger equations

Opened Access Soliton stability criterion for generalized nonlinear Schrödinger equations

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Autor: Quintero, Niurka R.
Mertens, Franz G.
Bishop, Alan R.
Departamento: Universidad de Sevilla. Departamento de Física Aplicada I
Fecha: 2015
Publicado en: Physical Review E, 91(1), 012905: 1-9
Tipo de documento: Artículo
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 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 asymmetr...
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Tamaño: 548.2Kb
Formato: PDF

URI: http://hdl.handle.net/11441/28044

DOI: 10.1103/PhysRevE.91.012905

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