The paper considers the vortex ring solutions of the nonlinear Schrödinger equation.For the nonlinear Schrödinger equation in two dimensions,we prove that the equations have a non-radial solution with arbitrarily specified number of zeros which decays exponentially at infinity,when the radial magnetic and electric potential satisfy appropriate sign conditions.In particular,classical physical situations such as the Coulomb potentials,inverse square potentials and steplike potentials satisfy our conditions.In order to prove the main result,besides using the shooting method to deal with the reduced ordinary differential equations,we mainly introduce a new Pohozaev identity,auxiliary functional and some appropriate function transformations.
关键词
非线性薛定谔方程/涡环解/常微分方程
Key words
nonlinear Schrödinger equation/vortex ring solution/ordinary differential equations
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