Higher Order Nonlinear Schrödinger Equation in Domains With Moving Boundaries

ABSTRACT The initial boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for a higher order nonlinear Schrödinger (HNLS) equation is considered. Existence and uniqueness of global weak solutions are proved as well as the stability of the solution. Additionally, a conservative numerical method of finite differences is introduced that also verifies stability properties with respect to the ‐norm, and along with proving its convergence, some interesting numerical examples are shown that illustrate the behavior of the solution.