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, Volume 13, Number 6,
pp. 593-601