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2013
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# N. Kostov

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

## Publications:

 Kostov N. A., Tsiganov A. V. New Lax pair for restricted multiple three wave interaction system, quasiperiodic solutions and bi-Hamiltonian structure 2008, vol. 13, no. 6, pp.  593-601 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. 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 DOI:10.1134/S1560354708060099