dorsal/arxiv
View SchemaBifurcating bright and dark solitary waves of the nearly nonlinear cubic-quintic Schrodinger equation
| Authors | Todd Kapitula |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9608009 |
| URL | https://arxiv.org/abs/patt-sol/9608009 |
Abstract
The existence of bright and dark multi-bump solitary waves for Ginzburg-Landau type perturbations of the cubic-quintic Schrodinger equation is considered. The waves in question are not perturbations of known analytic solitary waves, but instead arise as a bifurcation from a heteroclinic cycle in a three dimensional ODE phase space. Using geometric singular perturbation techniques, regions in parameter space for which 1-bump bright and dark solitary waves will bifurcate are identified. The existence of N-bump dark solitary waves is shown via an application of the Exchange Lemma with Exponentially Small Error. N-bump bright solitary waves are shown to exist as a consequence of the previous work of S. Maier-Paape and this author.
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"date_created": "2026-03-02T18:00:29.166000Z",
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"abstract": "The existence of bright and dark multi-bump solitary waves for\nGinzburg-Landau type perturbations of the cubic-quintic Schrodinger equation is\nconsidered. The waves in question are not perturbations of known analytic\nsolitary waves, but instead arise as a bifurcation from a heteroclinic cycle in\na three dimensional ODE phase space. Using geometric singular perturbation\ntechniques, regions in parameter space for which 1-bump bright and dark\nsolitary waves will bifurcate are identified. The existence of N-bump dark\nsolitary waves is shown via an application of the Exchange Lemma with\nExponentially Small Error. N-bump bright solitary waves are shown to exist as a\nconsequence of the previous work of S. Maier-Paape and this author.",
"arxiv_id": "patt-sol/9608009",
"authors": [
"Todd Kapitula"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"title": "Bifurcating bright and dark solitary waves of the nearly nonlinear cubic-quintic Schrodinger equation",
"url": "https://arxiv.org/abs/patt-sol/9608009"
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