Department of Mathematics, Shijiazhuang Railway Institute, Hebei, China
Department of Mathematics
Southern Polytechnic State University
1100 South Marietta Parkway
Marietta, GA 30060, USA
email: txu@spsu.edu
Zhongding Li, Taixi Xu
Abstract:
In this paper, we use the general Legendre transformation
to show the infinite dimensional integrable equations can be reduced
to a finite dimensional integrable Hamiltonian system on an invariant
set under the flow of the integrable equations. Then we obtain the
periodic or quasi-periodic solution of the equation. This generalizes
the results of Lax and Novikov regarding the periodic or
quasi-periodic solution of the KdV equation to the general case
of isospectral Hamiltonian integrable equation.
And finally, we discuss the AKNS hierarchy as a special example.
Submitted February 11, 2005. Published February 2, 2006.
Math Subject Classifications: 37K15, 37K40.
Key Words: Soliton equations; Hamiltonian equation;
Euler-Lagrange equation; integrable systems; Legendre transformation;
involutive system; symmetries of equations;
invariant manifold; Poisson bracket; symplectic space
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| Zhongding Li Department of Mathematics, Shijiazhuang Railway Institute, Hebei, China | |
|
Taixi Xu Department of Mathematics Southern Polytechnic State University 1100 South Marietta Parkway Marietta, GA 30060, USA email: txu@spsu.edu |
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