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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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Published in: | Chaos, solitons and fractals solitons and fractals, 2005-11, Vol.26 (3), p.979-996 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Citations: | Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0960-0779 1873-2887 |
DOI: | 10.1016/j.chaos.2005.02.006 |