Numerical study of transverse (in-)stability of solitary waves in the cubic-quintic nonlinear Schrödinger equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915579290451968 |
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| author | Klein, Christian Sparber, Christof |
| author_facet | Klein, Christian Sparber, Christof |
| contents | We study the nonlinear Schrödinger equation with a competing cubic-quintic power law nonlinearity on the waveguide domain $\mathbb R_x \times \mathbb T_{L_y}$. This model is globally well-posed and admits line solitary wave solutions, whose transverse (in-)stability is numerically investigated. We consider both spatially localized perturbations and periodic deformations of the line solitary wave and numerically confirm that there exists a critical torus length $L_y>0$ above which instability appears. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical study of transverse (in-)stability of solitary waves in the cubic-quintic nonlinear Schrödinger equation Klein, Christian Sparber, Christof Analysis of PDEs We study the nonlinear Schrödinger equation with a competing cubic-quintic power law nonlinearity on the waveguide domain $\mathbb R_x \times \mathbb T_{L_y}$. This model is globally well-posed and admits line solitary wave solutions, whose transverse (in-)stability is numerically investigated. We consider both spatially localized perturbations and periodic deformations of the line solitary wave and numerically confirm that there exists a critical torus length $L_y>0$ above which instability appears. |
| title | Numerical study of transverse (in-)stability of solitary waves in the cubic-quintic nonlinear Schrödinger equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.22735 |