Reduction of infinite dimensional equations

dc.contributor.authorLi, Zhongding
dc.contributor.authorXu, Taixi
dc.date.accessioned2021-07-14T18:51:50Z
dc.date.available2021-07-14T18:51:50Z
dc.date.issued2006-02-02
dc.description.abstractIn 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent15 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationLi, Z., & Xu, T. (2006). Reduction of infinite dimensional equations. <i>Electronic Journal of Differential Equations, 2006</i>(17), pp. 1-15.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/13890
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectSoliton equations
dc.subjectHamiltonian equation
dc.subjectEuler-Lagrange equation
dc.subjectIntegrable systems
dc.subjectLegendre transformation
dc.subjectInvolutive system
dc.subjectSymmetries of equations
dc.subjectInvariant manifold
dc.subjectPoisson bracket
dc.subjectSymplectic space
dc.titleReduction of infinite dimensional equations
dc.typeArticle

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