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Jones, C. (1988) Standing Waves of Nonlinear Schrödinger Equations: Existence and Stability, Material Instabilities in Continuum Mechanics (Edinburgh, 1985-86). Oxford University Press, Oxford, 197-216.

has been cited by the following article:

• TITLE: A Dirichlet Inhomogenous Boundary Value Problem for 1D Nonlinear Schrödinger Equation

  AUTHORS: Charles Bu

  KEYWORDS: Nonlinear Schrödinger Equation, Inhomogeneous Boundary Condition, Local Existence and Uniqueness

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.3, March 8, 2022

  ABSTRACT: Pure initial value problems for important nonlinear evolution equations such as nonlinear Schrödinger equation (NLS) and the Ginzburg-Landau equation (GL) have been extensively studied. However, many applications in physics lead to mathematical models where boundary data is inhomogeneous, e.g. in radio frequency wave experiments. In this paper, we investigate the mixed initial-boundary condition problem for the nonlinear Schrödinger equation iut = uxx – g|u|p-1u, g ∈ R, p > 3 on a semi-infinite strip. The equation satisfies an initial condition and Dirichlet boundary conditions. We utilize semi-group theory to prove existence and uniqueness theorem of a strong local solution.