1. On standing waves with a vortex point of order N for the nonlinear Chern–Simons–Schrödinger equations.
- Author
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Byeon, Jaeyoung, Huh, Hyungjin, and Seok, Jinmyoung
- Subjects
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STANDING waves , *VORTEX methods , *NONLINEAR equations , *CHERN-Simons gauge theory , *EXISTENCE theorems , *MATHEMATICAL proofs - Abstract
In this paper, we are interested in standing waves with a vortex for the nonlinear Chern–Simons–Schrödinger equations (CSS for short). We study the existence and the nonexistence of standing waves when a constant λ > 0 , representing the strength of the interaction potential, varies. We prove every standing wave is trivial if λ ∈ ( 0 , 1 ) , every standing wave is gauge equivalent to a solution of the first order self-dual system of CSS if λ = 1 and for every positive integer N , there is a nontrivial standing wave with a vortex point of order N if λ > 1 . We also provide some classes of interaction potentials under which the nonexistence of standing waves and the existence of a standing wave with a vortex point of order N are proved. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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