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