Existence and orbital stability of standing waves for some nonlinear Schrodinger equations, perturbation of a model case

François Samer Genoud
2009
Journal paper

Abstract

The following nonlinear Schrodinger equation is studied

Official source

https://infoscience.epfl.ch/record/160037?ln=en

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We study the Cauchy problem for the one-dimensional wave equation

\partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0.

The potential

V

is assumed to be smooth with asymptotic behavior

V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty.

...

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