Higher Order Nonlinear Schrödinger Equation in Domains With Moving Boundaries

Nina-Mollisaca R.; Sepúlveda-Cortés M.; Véjar-Asem R.; Vera-Villagrán O. · Mathematical Methods in the Applied Sciences (2025) · DOI: 10.1002/mma.11000

Resumen

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 (Formula presented.) -norm, and along with proving its convergence, some interesting numerical examples are shown that illustrate the behavior of the solution.

Instituciones: Universidad Nacional Jorge Basadre Grohmann