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arXiv · 2406.18793

Higher order nonlinear Schr\"odinger equation in domains with moving boundaries

Raul Nina Mollisaca·Mauricio Sepúlveda Cortés·Rodfigo Véjar Asém·Octavio Vera Villagrán
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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 $L^2$-norm, and along with proving its convergence, some interesting numerical examples are shown that illustrate the behavior of the solution.

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Raul Nina Mollisaca, Mauricio Sepúlveda Cortés, Rodfigo Véjar Asém, Octavio Vera Villagrán. 2024-06-26. Higher order nonlinear Schr\"odinger equation in domains with moving boundaries. https://doi.org/10.1002/mma.11000

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