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

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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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Though obliquely incident plane wave across rock fractures has been extensively investigated by theoretical analysis, the quantitative identification of each wave emerged from fractures has not been achieved either in numerical simulation or laboratory exp ...

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

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