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Forced nonlinear Schrödinger equation with arbitrary nonlinearity

Opened Access Forced nonlinear Schrödinger equation with arbitrary nonlinearity


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Autor: Cooper, Fred
Khare, Avinash
Quintero, Niurka R.
Mertens, Franz G.
Saxena, Avadh
Departamento: Universidad de Sevilla. Departamento de Física Aplicada I
Fecha: 2012
Publicado en: Physical Review E, 2012, 85(4), 046607: 1-24
Tipo de documento: Artículo
Resumen: We consider the nonlinear Schrödinger equation (NLSE) in 1+1 dimension with scalar-scalar self-interaction g2κ+1(ψ☆ψ)κ+1 in the presence of the external forcing terms of the form re−i(kx+θ)−δψ. We find new exact solutions for this problem and show that the solitary wave momentum is conserved in a moving frame where vk=2k. These new exact solutions reduce to the constant phase solutions of the unforced problem when r→0. In particular we study the behavior of solitary wave solutions in the presence of these external forces in a variational approximation which allows the position, momentum, width, and phase of these waves to vary in time. We show that the stationary solutions of the variational equations include a solution close to the exact one and we study small oscillations around all the stationary solutions. We postulate that the dynamical condition for instability is that dp(t)/dq̇ (t)<0, where p(t) is the normalized canonical momentum p(t)=1M(t)∂L∂q̇ , and q̇ (t) is the solitary w...
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DOI: 10.1103/PhysRevE.85.046607

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