New lax pair for restricted multiple three wave interaction system, quasiperiodic solutions and bi-Hamiltonian structure
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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.
Key wordsLax pair bi-Hamiltonian structure three wave interaction system
MSC2000 numbers37K10 70E20 70E4