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An algebro-geometric solution for a Hamiltonian system with application to dispersive long wave equation

注意：本论文已在JOURNAL OF MATHEMATICAL PHYSICS ，46, 032701, 2005:1-21发表
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Y. C. Hon(a)
Department of Mathematics, City University of Hong Kong, Hong Kong SAR, People’s Republic of China
E. G. Fan(b)
Institute of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China
(Received 14 October 2003; accepted 3 December 2004; published online 8 February 2005)

Abstract:By using an iterative algebraic method, we derive from a spectral problem a hierarchy of nonlinear evolution equations associated with dispersive long wave equation. It is shown that the hierarchy is integrable in Liouville sense and possesses bi-Hamiltonian structure. Two commutators, with zero curvature and Lax representations,for the hierarchy are constructed, respectively, by using two different systematic methods. Under a Bargmann constraint the spectral is nonlinearized to a completely integrable finite dimensional Hamiltonian system. By introducing the Abel–Jacobi coordinates, an algebro-geometric solution for the dispersive long wave equation is derived by resorting to the Riemann theta function.

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