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Nonlinear Schrödinger equation with spatiotemporal perturbations

Opened Access Nonlinear Schrödinger equation with spatiotemporal perturbations


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Autor: Mertens, Franz G.
Quintero, Niurka R.
Bishop, Alan R.
Departamento: Universidad de Sevilla. Departamento de Física Aplicada I
Fecha: 2010
Publicado en: Physical Review E, 2010, 81(1), 016608: 1-11
Tipo de documento: Artículo
Resumen: We investigate the dynamics of solitons of the cubic nonlinear Schrödinger equation (NLSE) with the following perturbations: nonparametric spatiotemporal driving of the form f(x,t)=a exp[iK(t)x], damping, and a linear term which serves to stabilize the driven soliton. Using the time evolution of norm, momentum and energy, or, alternatively, a Lagrangian approach, we develop a collective-coordinate-theory which yields a set of ordinary differential equations (ODEs) for our four collective coordinates. These ODEs are solved analytically and numerically for the case of a constant, spatially periodic force f(x). The soliton position exhibits oscillations around a mean trajectory with constant velocity. This means that the soliton performs, on the average, a unidirectional motion although the spatial average of the force vanishes. The amplitude of the oscillations is much smaller than the period of f(x). In order to find out for which regions the above solutions are stable, we calculate th...
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Tamaño: 626.6Kb
Formato: PDF


DOI: 10.1103/PhysRevE.81.016608

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