Artículo
Response of exact solutions of the nonlinear Schrödinger equation to small perturbations in a class of complex external potentials having supersymmetry and parity-time symmetry
Autor/es | Cooper, Fred
Dawson, John F. Mertens, Franz G. Arévalo, Edward Quintero, Niurka R. Mihaila, Bogdan Khare, Avinash Saxena, Avadh |
Departamento | Universidad de Sevilla. Departamento de Física Aplicada I |
Fecha de publicación | 2017 |
Fecha de depósito | 2018-11-23 |
Publicado en |
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Resumen | We discuss the effect of small perturbation on nodeless solutions of
the nonlinear Schrödinger equation in 1 + 1 dimensions in an external
complex potential derivable from a parity-time symmetric superpotential
that ... We discuss the effect of small perturbation on nodeless solutions of the nonlinear Schrödinger equation in 1 + 1 dimensions in an external complex potential derivable from a parity-time symmetric superpotential that was considered earlier (Kevrekidis et al 2015 Phys. Rev. E 92 042901). In particular, we consider the nonlinear partial differential equation { i ∂t + ∂2 x + g|ψ(x, t)| 2 − V+(x) } ψ(x, t) = 0, where V+(x)=(−b2 − m2 + 1/4)sech2 (x) − 2i m b sech(x) tanh(x) represents the complex potential. Here, we study the perturbations as a function of b and m using a variational approximation based on a dissipation functional formalism. We compare the result of this variational approach with direct numerical simulation of the equations. We find that the variational approximation works quite well at small and moderate values of the parameter product bm which controls the strength of the imaginary part of the potential. We also show that the dissipation functional formalism is equivalent to the generalized traveling wave method for this type of dissipation. |
Identificador del proyecto | FIS2014- 54497-P
FQM207 P11-FQM-7276 1141223 130001 |
Cita | Cooper, F., Dawson, J.F., Mertens, F.G., Arévalo, E., Quintero, N.R., Mihaila, B.,...,Saxena, A. (2017). Response of exact solutions of the nonlinear Schrödinger equation to small perturbations in a class of complex external potentials having supersymmetry and parity-time symmetry. Journal of Physics A: Mathematical and Theoretical, 50, 485205-. |
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