N. Kostov

Blvd. Tzarigradsko chaussee 72, 1784 Sofia, Bulgaria
Institute for Electronics, Bulgarian Academy of Sciences


Kostov N. A., Tsiganov A. V.
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.
Keywords: Lax pair, bi-Hamiltonian structure, three wave interaction system
Citation: Kostov N. A., Tsiganov A. V.,  New Lax pair for restricted multiple three wave interaction system, quasiperiodic solutions and bi-Hamiltonian structure, Regular and Chaotic Dynamics, 2008, vol. 13, no. 6, pp. 593-601

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