Strong instability of solitary waves for inhomogeneous nonlinear Schrödinger equations. (English) Zbl 1479.35828

Summary: This paper studies the inhomogeneous nonlinear Schrödinger equations, which may model the propagation of laser beams in nonlinear optics. Using the cross-constrained variational method, a sharp condition for global existence is derived. Then, by solving a variational problem, the strong instability of solitary waves of this equation is proved.


35Q55 NLS equations (nonlinear Schrödinger equations)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35A15 Variational methods applied to PDEs
35C08 Soliton solutions
35B35 Stability in context of PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
78A60 Lasers, masers, optical bistability, nonlinear optics
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