Small-amplitude self-similar solutions for one-dimensional nonlinear dispersive equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915625758097408 |
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| author | Correia, Simão Pereira, Gonçalo Santos, Thyago S. R. |
| author_facet | Correia, Simão Pereira, Gonçalo Santos, Thyago S. R. |
| contents | Given a nonlinear dispersive equation which admits a scaling invariance, there may exist self-similar solutions. In this work, we present a systematic approach for the construction of small-amplitude self-similar solutions, together with precise asymptotic descriptions at both small and large frequency scales. These ideas are then applied to three classic dispersive models: the modified Benjamin-Ono, the quartic Korteweg-de Vries and the cubic nonlinear Schrödinger equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_14586 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Small-amplitude self-similar solutions for one-dimensional nonlinear dispersive equations Correia, Simão Pereira, Gonçalo Santos, Thyago S. R. Analysis of PDEs Given a nonlinear dispersive equation which admits a scaling invariance, there may exist self-similar solutions. In this work, we present a systematic approach for the construction of small-amplitude self-similar solutions, together with precise asymptotic descriptions at both small and large frequency scales. These ideas are then applied to three classic dispersive models: the modified Benjamin-Ono, the quartic Korteweg-de Vries and the cubic nonlinear Schrödinger equations. |
| title | Small-amplitude self-similar solutions for one-dimensional nonlinear dispersive equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.14586 |