On orbital stability of the physical ground states of the NLS equations

2021/03/30 by Il'yasov, Yavdat
#35A15 #35B35 35A01 #35J61 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.16353

Abstract

We prove orbital stability result for physical ground states of a nonlinear Schrödinger (NLS) equation in the sense that the set of these ground states is contained in the set of prescribed mass solutions which is orbital stable by the Cazenave-Lions theorem. We apply the nonlinear generalized Rayleigh quotients method which allows establishing a one-to-one correspondence between the values of the mass m, the frequency λ, and the action level S of the physical ground states.

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