Regular and Chaotic Dynamics

, Volume 13, Issue 6, pp 593–601 | Cite as

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

Jürgen Moser - 80

Abstract

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 words

Lax pair bi-Hamiltonian structure three wave interaction system 

MSC2000 numbers

37K10 70E20 70E4 

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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.Institute for ElectronicsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Department of Mathematical and Computational PhysicsSt. Petersburg State UniversitySt. PetersburgRussia

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