dorsal/arxiv
View SchemaSelf-similar solutions of NLS-type dynamical systems
| Authors | M. Boiti, V. G. Marikhin, F. Pempinelli, A. B. Shabat |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9909021 |
| URL | https://arxiv.org/abs/solv-int/9909021 |
Abstract
We study self-similar solutions of NLS-type dynamical systems. Lagrangian approach is used to show that they can be reduced to three canonical forms, which are related by Miura transformations. The fourth Painleve equation (PIV) is central in our consideration - it connects Heisenberg model, Volterra model and Toda model to each other. The connection between the rational solutions of PIV and Coulomb gas in a parabolic potential is established. We discuss also the possibility to obtain an exact solution for optical soliton i.e. of the NLS equation with time-dependent dispersion.
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"abstract": "We study self-similar solutions of NLS-type dynamical systems. Lagrangian\napproach is used to show that they can be reduced to three canonical forms,\nwhich are related by Miura transformations. The fourth Painleve equation (PIV)\nis central in our consideration - it connects Heisenberg model, Volterra model\nand Toda model to each other. The connection between the rational solutions of\nPIV and Coulomb gas in a parabolic potential is established. We discuss also\nthe possibility to obtain an exact solution for optical soliton i.e. of the NLS\nequation with time-dependent dispersion.",
"arxiv_id": "solv-int/9909021",
"authors": [
"M. Boiti",
"V. G. Marikhin",
"F. Pempinelli",
"A. B. Shabat"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Self-similar solutions of NLS-type dynamical systems",
"url": "https://arxiv.org/abs/solv-int/9909021"
},
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