Reduction of infinite dimensional equations
dc.contributor.author | Li, Zhongding | |
dc.contributor.author | Xu, Taixi | |
dc.date.accessioned | 2021-07-14T18:51:50Z | |
dc.date.available | 2021-07-14T18:51:50Z | |
dc.date.issued | 2006-02-02 | |
dc.description.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. | |
dc.description.department | Mathematics | |
dc.format | Text | |
dc.format.extent | 15 pages | |
dc.format.medium | 1 file (.pdf) | |
dc.identifier.citation | Li, Z., & Xu, T. (2006). Reduction of infinite dimensional equations. Electronic Journal of Differential Equations, 2006(17), pp. 1-15. | |
dc.identifier.issn | 1072-6691 | |
dc.identifier.uri | https://hdl.handle.net/10877/13890 | |
dc.language.iso | en | |
dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
dc.rights | Attribution 4.0 International | |
dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.source | Electronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
dc.subject | Soliton equations | |
dc.subject | Hamiltonian equation | |
dc.subject | Euler-Lagrange equation | |
dc.subject | Integrable systems | |
dc.subject | Legendre transformation | |
dc.subject | Involutive system | |
dc.subject | Symmetries of equations | |
dc.subject | Invariant manifold | |
dc.subject | Poisson bracket | |
dc.subject | Symplectic space | |
dc.title | Reduction of infinite dimensional equations | |
dc.type | Article |