dorsal/arxiv
View SchemaKorteweg-de Vries hierarchy and related completely integrable systems: I. Algebro-geometrical approach
| Authors | N. A. Kostov |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9904016 |
| URL | https://arxiv.org/abs/solv-int/9904016 |
Abstract
We consider complementary dynamical systems related to stationary Korteweg-de Vries hierarchy of equations. A general approach for finding elliptic solutions is given. The solutions are expressed in terms of Novikov polynomials in general quais-periodic case. For periodic case these polynomials coincide with Hermite and Lam\'e polynomials. As byproduct we derive $2\times 2$ matrix Lax representation for Rosochatius-Wojciechiwski, Rosochatius, second flow of stationary nonlinear vectro Schr\"{o}dinger equations and complex Neumann system.
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"abstract": "We consider complementary dynamical systems related to stationary Korteweg-de\nVries hierarchy of equations. A general approach for finding elliptic solutions\nis given. The solutions are expressed in terms of Novikov polynomials in\ngeneral quais-periodic case. For periodic case these polynomials coincide with\nHermite and Lam\\\u0027e polynomials. As byproduct we derive $2\\times 2$ matrix Lax\nrepresentation for Rosochatius-Wojciechiwski, Rosochatius, second flow of\nstationary nonlinear vectro Schr\\\"{o}dinger equations and complex Neumann\nsystem.",
"arxiv_id": "solv-int/9904016",
"authors": [
"N. A. Kostov"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Korteweg-de Vries hierarchy and related completely integrable systems: I. Algebro-geometrical approach",
"url": "https://arxiv.org/abs/solv-int/9904016"
},
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