Geodesic
Reduction of infinite dimensional equations
Electronic Journal of Differential Equations, Tome 2006 (2006).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 37K15, 37K40
Keywords: 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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     author = {Li, Zhongding and Xu, Taixi},
     title = {Reduction of infinite dimensional equations},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2006},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a177/}
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Li, Zhongding; Xu, Taixi. Reduction of infinite dimensional equations. Electronic Journal of Differential Equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a177/