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arXiv · 0705.4363

New Lax pair for restricted multiple three wave interaction system, quasiperiodic solutions and bi-hamiltonian structure

N. A. Kostov·A. V. Tsiganov
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Abstract

We study restricted multiple three wave interaction system by the inverse scattering method. We develop the algebraic approach in terms of classical $r$-matrix and give an interpretation of the Poisson brackets as linear $r$-matrix algebra. The solutions are expressed in terms of polynomials of theta functions. In particular case for $n=1$ in terms of Weierstrass functions.

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N. A. Kostov, A. V. Tsiganov. 2007-05-30. New Lax pair for restricted multiple three wave interaction system, quasiperiodic solutions and bi-hamiltonian structure. https://doi.org/10.1134/s1560354708060099

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