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

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  • Y. C. Hon
  • E. G. Fan

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Original languageEnglish
Article number32701
Journal / PublicationJournal of Mathematical Physics
Issue number3
Publication statusPublished - Mar 2005


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. © 2005 American Institute of Physics.