Orbital stability of kinks in the NLS equation with competing nonlinearities
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912755775176704 |
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| author | Holmer, Justin Kevrekidis, Panayotis G. Pelinovsky, Dmitry E. |
| author_facet | Holmer, Justin Kevrekidis, Panayotis G. Pelinovsky, Dmitry E. |
| contents | Kinks connecting zero and nonzero equilibria in the NLS equation with competing nonlinearities occur at the special values of the frequency parameter. Since they are minimizers of energy, they are expected to be orbitally stable in the time evolution of the NLS equation. However, the stability proof is complicated by the degeneracy of kinks near the nonzero equilibrium. The main purpose of this work is to give a rigorous proof of the orbital stability of kinks. We give details of analysis for the cubic--quintic NLS equation and show how the proof is extended to the general case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_08840 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orbital stability of kinks in the NLS equation with competing nonlinearities Holmer, Justin Kevrekidis, Panayotis G. Pelinovsky, Dmitry E. Analysis of PDEs Pattern Formation and Solitons Kinks connecting zero and nonzero equilibria in the NLS equation with competing nonlinearities occur at the special values of the frequency parameter. Since they are minimizers of energy, they are expected to be orbitally stable in the time evolution of the NLS equation. However, the stability proof is complicated by the degeneracy of kinks near the nonzero equilibrium. The main purpose of this work is to give a rigorous proof of the orbital stability of kinks. We give details of analysis for the cubic--quintic NLS equation and show how the proof is extended to the general case. |
| title | Orbital stability of kinks in the NLS equation with competing nonlinearities |
| topic | Analysis of PDEs Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2512.08840 |