Vortex ring solutions of a class of nonlinear Schr?dinger equations
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.
nonlinear Schrödinger equationvortex ring solutionordinary differential equations
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维普
