Steady-state solutions for Schrödinger equations in photonic lattice
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Date
2018-05-08
Authors
Li, Wen-Long
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study a nonlinear Schrödinger equation arising in optics. Firstly we prove the existence of multiple solutions of this equation. Secondly, we consider a nonlinear Schrödinger system which is intimately related to the Schrödinger equation. We obtain the existence of nontrivial solutions to this system and we also get some results on its positive solutions. Finally, assuming Dirichlet or Neumann boundary condition, we show the existence and uniqueness of positive solution to the Schrödinger equation.
Description
Keywords
Schrödinger equation, Multiple solutions, Positive solutions, Nontrivial solutions
Citation
Li, W. L. (2018). Steady-state solutions for Schrödinger equations in photonic lattice. <i>Electronic Journal of Differential Equations, 2018</i>(109), pp. 1-12.
Rights
Attribution 4.0 International