Reduction of infinite dimensional equations
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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.
CitationLi, Z., & Xu, T. (2006). Reduction of infinite dimensional equations. Electronic Journal of Differential Equations, 2006(17), pp. 1-15.
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