Higher order nonlinear Schr\"odinger equation in domains with moving boundaries
Analysis of PDEs
2025-05-07 v1
Abstract
The initial-boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for a higher order nonlinear Schr\"odinger (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.
Keywords
Cite
@article{arxiv.2406.18793,
title = {Higher order nonlinear Schr\"odinger equation in domains with moving boundaries},
author = {Raul Nina Mollisaca and Mauricio Sepúlveda Cortés and Rodfigo Véjar Asém and Octavio Vera Villagrán},
journal= {arXiv preprint arXiv:2406.18793},
year = {2025}
}