Response of exact solutions of the nonlinear Schrodinger equation to small perturbations in a class of complex external potentials having supersymmetry and parity-time symmetry
| Autor: | Bogdan Mihaila, Fred Cooper, Niurka R. Quintero, Franz G. Mertens, Avadh Saxena, Edward Arévalo, John F. Dawson, Avinash Khare |
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| Přispěvatelé: | Universidad de Sevilla. Departamento de Física Aplicada I, Universidad de Sevilla. FQM-207 Física Atómica y Molecular |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Direct numerical simulation General Physics and Astronomy FOS: Physical sciences Pattern Formation and Solitons (nlin.PS) Traveling wave method 01 natural sciences 010305 fluids & plasmas symbols.namesake 0103 physical sciences 010306 general physics Nonlinear Schrödinger equation Mathematical Physics Mathematical physics Physics Dissipation functional Variational approach Hyperbolic function Superpotential Stability analysis Collective coordinates Statistical and Nonlinear Physics Parity (physics) Supersymmetry Nonlinear Sciences - Pattern Formation and Solitons Nonlinear system Modeling and Simulation symbols Schrödinger's cat |
| Zdroj: | idUS. Depósito de Investigación de la Universidad de Sevilla instname |
| DOI: | 10.48550/arxiv.1707.01574 |
| Popis: | We discuss the effect of small perturbation on nodeless solutions of the nonlinear \Schrodinger\ equation in 1+1 dimensions in an external complex potential derivable from a parity-time symmetric superpotential that was considered earlier [Phys.~Rev.~E 92, 042901 (2015)]. In particular we consider the nonlinear partial differential equation $\{ \, \rmi \, \partial_t + \partial_x^2 + g |\psi(x,t)|^2 - V^{+}(x) \, \} \, \psi(x,t) = 0$, where $V^{+}(x) = \qty( -b^2 - m^2 + 1/4 ) \, \sech^2(x) - 2 i \, m \, b \, \sech(x) \, \tanh(x)$ 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 $b m$ 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. Comment: 18 pages, 6 figures |
| Databáze: | OpenAIRE |
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