Li, ZhongdingXu, Taixi2021-07-142021-07-142006-02-02Li, Z., & Xu, T. (2006). Reduction of infinite dimensional equations. <i>Electronic Journal of Differential Equations, 2006</i>(17), pp. 1-15.1072-6691https://hdl.handle.net/10877/13890In 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.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalSoliton equationsHamiltonian equationEuler-Lagrange equationIntegrable systemsLegendre transformationInvolutive systemSymmetries of equationsInvariant manifoldPoisson bracketSymplectic spaceArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.