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

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

2007-05-30

arxiv.org/abs/0705.4363v2

Regular and Chaotic Dynamics, v.13, n.6, pp. 593-601, 2008

Nonlinear Sciences

Exactly Solvable and Integrable Systems

8 pages, revtex4, corrected typos

Scientific paper

10.1134/S1560354708060099

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.

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