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Korteweg-de Vries hierarchy and related completely integrable systems: I. Algebro-geometrical approach

N. A. Kostov
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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 Lamé polynomials. As byproduct we derive $2\times 2$ matrix Lax representation for Rosochatius-Wojciechiwski, Rosochatius, second flow of stationary nonlinear vectro Schrödinger equations and complex Neumann system.

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BibTeXRIS

N. A. Kostov. 1999-04-16. Korteweg-de Vries hierarchy and related completely integrable systems: I. Algebro-geometrical approach. https://arxiv.org/abs/solv-int/9904016

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