Open AccessCross-constrained variational method and nonlinear Schrödinger equation with partial confinement
Author(s) -
Zhong Chen,
Jian Zhang
Publication year - 2022
Publication title -
mathematical control and related fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.658
H-Index - 21
eISSN - 2156-8472
pISSN - 2156-8499
DOI - 10.3934/mcrf.2021036
Subject(s) - invariant (physics) , nonlinear system , mathematics , nonlinear schrödinger equation , mathematical physics , partial differential equation , mathematical analysis , schrödinger equation , physics , quantum mechanics
In this paper, we study the nonlinear Schrödinger equation with a partial confinement. By applying the cross-constrained variational arguments and invariant manifolds of the evolution flow, the sharp condition for global existence and blowup of the solution is derived.