Steady-state solutions for Schrodinger equations in photonic lattice

Abstract

In this article, we study a nonlinear Schrodinger equation arising in optics. Firstly we prove the existence of multiple solutions of this equation. Secondly, we consider a nonlinear Schrodinger system which is intimately related to the Schrodinger 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 Schrodinger equation.

Keywords

• Schrodinger equation
• multiple solutions
• positive solution
• nontrivial solution