On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation
In this paper, we consider the reducibility of the quasiperiodic linear Hamiltonian system ẋ=A+εQt, where A is a constant matrix with possible multiple eigenvalues, Qt is analytic quasiperiodic with respect to t, and ε is a small parameter. Under some nonresonant conditions, it is proved that, for...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/6260253 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832546852405248000 |
|---|---|
| author | Nina Xue Wencai Zhao |
| author_facet | Nina Xue Wencai Zhao |
| author_sort | Nina Xue |
| collection | DOAJ |
| description | In this paper, we consider the reducibility of the quasiperiodic linear Hamiltonian system ẋ=A+εQt, where A is a constant matrix with possible multiple eigenvalues, Qt is analytic quasiperiodic with respect to t, and ε is a small parameter. Under some nonresonant conditions, it is proved that, for most sufficiently small ε, the Hamiltonian system can be reduced to a constant coefficient Hamiltonian system by means of a quasiperiodic symplectic change of variables with the same basic frequencies as Qt. Applications to the Schrödinger equation are also given. |
| format | Article |
| id | doaj-art-0a4423d02a474fcca196e477117c8ea0 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-0a4423d02a474fcca196e477117c8ea02025-02-03T06:46:53ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/62602536260253On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger EquationNina Xue0Wencai Zhao1School of Mathematics and Information Sciences, Weifang University, Weifang 261061, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, ChinaIn this paper, we consider the reducibility of the quasiperiodic linear Hamiltonian system ẋ=A+εQt, where A is a constant matrix with possible multiple eigenvalues, Qt is analytic quasiperiodic with respect to t, and ε is a small parameter. Under some nonresonant conditions, it is proved that, for most sufficiently small ε, the Hamiltonian system can be reduced to a constant coefficient Hamiltonian system by means of a quasiperiodic symplectic change of variables with the same basic frequencies as Qt. Applications to the Schrödinger equation are also given.http://dx.doi.org/10.1155/2020/6260253 |
| spellingShingle | Nina Xue Wencai Zhao On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation Journal of Function Spaces |
| title | On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation |
| title_full | On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation |
| title_fullStr | On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation |
| title_full_unstemmed | On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation |
| title_short | On the Reducibility of Quasiperiodic Linear Hamiltonian Systems and Its Applications in Schrödinger Equation |
| title_sort | on the reducibility of quasiperiodic linear hamiltonian systems and its applications in schrodinger equation |
| url | http://dx.doi.org/10.1155/2020/6260253 |
| work_keys_str_mv | AT ninaxue onthereducibilityofquasiperiodiclinearhamiltoniansystemsanditsapplicationsinschrodingerequation AT wencaizhao onthereducibilityofquasiperiodiclinearhamiltoniansystemsanditsapplicationsinschrodingerequation |