Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 17, pp. 1-15.

Title: Reduction of infinite dimensional equations
       
Authors: Zhongding Li (Shijiazhuang Railway Institute, Hebei, China)
         Taixi Xu (Southern Polytechnic State Univ., Marietta, GA, USA)

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