Reduction of infinite dimensional equations
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Date
2006-02-02
Authors
Li, Zhongding
Xu, Taixi
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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.
Description
Keywords
Soliton equations, Hamiltonian equation, Euler-Lagrange equation, Integrable systems, Legendre transformation, Involutive system, Symmetries of equations, Invariant manifold, Poisson bracket, Symplectic space
Citation
Li, Z., & Xu, T. (2006). Reduction of infinite dimensional equations. <i>Electronic Journal of Differential Equations, 2006</i>(17), pp. 1-15.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.