Steady-state solutions for Schrödinger equations in photonic lattice

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. Electronic Journal of Differential Equations, 2018(109), pp. 1-12.

Rights

Attribution 4.0 International

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