N. Kostov
Blvd. Tzarigradsko chaussee 72, 1784 Sofia, Bulgaria
Institute for Electronics, Bulgarian Academy of Sciences
Publications:
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Kostov N. A., Tsiganov A. V.
New Lax pair for restricted multiple three wave interaction system, quasiperiodic solutions and bi-Hamiltonian structure
2008, vol. 13, no. 6, pp. 593-601
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.
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