Higher order nonlinear Schrödinger equation in domains with moving boundaries
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866913821614931968 |
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| author | Mollisaca, Raul Nina Cortés, Mauricio Sepúlveda Asém, Rodfigo Véjar Villagrán, Octavio Vera |
| author_facet | Mollisaca, Raul Nina Cortés, Mauricio Sepúlveda Asém, Rodfigo Véjar Villagrán, Octavio Vera |
| contents | 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 $L^2$-norm, and along with proving its convergence, some interesting numerical examples are shown that illustrate the behavior of the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18793 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher order nonlinear Schrödinger equation in domains with moving boundaries Mollisaca, Raul Nina Cortés, Mauricio Sepúlveda Asém, Rodfigo Véjar Villagrán, Octavio Vera Analysis of PDEs 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 $L^2$-norm, and along with proving its convergence, some interesting numerical examples are shown that illustrate the behavior of the solution. |
| title | Higher order nonlinear Schrödinger equation in domains with moving boundaries |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.18793 |