Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 50, Issue 48, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/aa8d25
Keywords
stability analysis; collective coordinates; variational approach; dissipation functional; traveling wave method
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Funding
- Ministerio de Economia y Competitividad (Spain) [FIS2014-54497-P]
- Plan Propio of Universidad de Seville
- Theoretical Division at Los Alamos National Laboratory
- Center for Nonlinear Studies at Los Alamos National Laboratory
- Junta de Andalucia (Spain) [FQM207, P11-FQM-7276]
- Fondo Nacional de Desarrollo Cientifico y Tecnologico (FONDECYT) project [1141223]
- Programa Iniciativa Cientfica Milenio (ICM) Grant [130001]
- Indian National Science Academy (INSA)
- National Science Foundation through its employee IR/D program
- US Department of Energy
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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 (Kevrekidis et al 2015 Phys. Rev. E 92 042901). In particular, we consider the nonlinear partial differential equation {i partial derivative(t) + partial derivative(2)(x) + g vertical bar psi(x, t)vertical bar(2) - V+(x)} psi(x, t) = 0, where V+(x) = (-b(2) - m(2) + 1/4) sech(2)(x) - 2imb 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.
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