On the solvability of initial boundary value problems for nonlinear time-dependent Schrödinger equations

Abstract

In this paper, we study the initial boundary value problems for a nonlinear time-dependent Schrödinger equation with Dirichlet and Neumann boundary conditions, respectively. We prove the existence and uniqueness of solutions of the initial boundary value problems by using Galerkin’s method.

Mathematics Subject Classification (2010):

• 35Q41
• 35K20
• 35A01

Key words:

• Initial boundary value problem
• nonlinear time-dependent Schrödinger equation
• Galerkin’s method