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This article is cited in 3 scientific papers (total in 3 papers)
JÜRGEN MOSER – 80
New Lax pair for restricted multiple three wave interaction system, quasiperiodic solutions and bi-Hamiltonian structure
N.A. Kostova, A. V. Tsiganovb a Institute for Electronics, Bulgarian Academy of Sciences,
Blvd. Tzarigradsko chaussee 72, 1784 Sofia, Bulgaria
b Department of Mathematical and Computational Physics,
St. Petersburg State University, Russia
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.
Keywords:
Lax pair, bi-Hamiltonian structure, three wave interaction system.
Received: 28.08.2008 Accepted: 12.10.2008
Citation:
N.A. Kostov, A. V. Tsiganov, “New Lax pair for restricted multiple three wave interaction system, quasiperiodic solutions and bi-Hamiltonian structure”, Regul. Chaotic Dyn., 13:6 (2008), 593–601
Linking options:
https://www.mathnet.ru/eng/rcd604 https://www.mathnet.ru/eng/rcd/v13/i6/p593
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