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We study restricted multiple three wave interaction system by the inversescattering 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 oftheta functions. In particular case for $n=1$ in terms of Weierstrassfunctions.

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