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Two (2 + 1)-dimensional soliton equations and their quasi-periodic solutions

Two (2 + 1)-dimensional soliton equations and their decomposition into the mixed (1 + 1)-dimensional soliton equations are proposed. With the help of nonlinearization approach, the Lenard spectral problem related to the mixed soliton hierarchy is turned into a completely integrable Hamiltonian syste...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2005-11, Vol.26 (3), p.979-996
Main Authors: Hao, Yanhong, Du, Dianlou
Format: Article
Language:English
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Summary:Two (2 + 1)-dimensional soliton equations and their decomposition into the mixed (1 + 1)-dimensional soliton equations are proposed. With the help of nonlinearization approach, the Lenard spectral problem related to the mixed soliton hierarchy is turned into a completely integrable Hamiltonian system with a Lie–Poisson structure on the Poisson manifold R 3 N . The Abel–Jacobi coordinates are introduced to straighten out the Hamiltonian flows. Based on the decomposition and the theory of algebra curve, the explicit quasi-periodic solutions for the (1 + 1)- and (2 + 1)-dimensional soliton equations are obtained.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2005.02.006