A Hyperbolic Approximation of the Nonlinear Schrödinger Equation
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916762011828224 |
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| author | Biswas, Abhijit Busaleh, Laila S. Ketcheson, David I. Muñoz-Moncayo, Carlos Rajvanshi, Manvendra |
| author_facet | Biswas, Abhijit Busaleh, Laila S. Ketcheson, David I. Muñoz-Moncayo, Carlos Rajvanshi, Manvendra |
| contents | We study a first-order hyperbolic approximation of
the nonlinear Schrödinger (NLS) equation. We show that the system
is strictly hyperbolic and possesses a modified Hamiltonian structure, along with
at least three conserved quantities that approximate those of NLS.
We provide families of explicit standing-wave solutions to the hyperbolic system,
which are shown to converge uniformly to ground-state solutions
of NLS in the relaxation limit.
The system is formally equivalent to NLS in the relaxation limit, and we
develop asymptotic preserving discretizations that tend to a consistent discretization
of NLS in that limit, while also conserving mass.
Examples for both the focusing and defocusing regimes demonstrate that the
numerical discretization provides an accurate approximation of the NLS
solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21424 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Hyperbolic Approximation of the Nonlinear Schrödinger Equation Biswas, Abhijit Busaleh, Laila S. Ketcheson, David I. Muñoz-Moncayo, Carlos Rajvanshi, Manvendra Analysis of PDEs Numerical Analysis Mathematical Physics Computational Physics We study a first-order hyperbolic approximation of the nonlinear Schrödinger (NLS) equation. We show that the system is strictly hyperbolic and possesses a modified Hamiltonian structure, along with at least three conserved quantities that approximate those of NLS. We provide families of explicit standing-wave solutions to the hyperbolic system, which are shown to converge uniformly to ground-state solutions of NLS in the relaxation limit. The system is formally equivalent to NLS in the relaxation limit, and we develop asymptotic preserving discretizations that tend to a consistent discretization of NLS in that limit, while also conserving mass. Examples for both the focusing and defocusing regimes demonstrate that the numerical discretization provides an accurate approximation of the NLS solution. |
| title | A Hyperbolic Approximation of the Nonlinear Schrödinger Equation |
| topic | Analysis of PDEs Numerical Analysis Mathematical Physics Computational Physics |
| url | https://arxiv.org/abs/2505.21424 |