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

Wang, Chenglin; Zhang, Jian

Math. Methods Appl. Sci. 44, No. 18, 14632-14642 (2021).

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.

MSC:

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

Keywords:

inhomogeneous nonlinear Schrödinger equation; instability; sharp condition; variational problem; solitary wave