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http://hdl.handle.net/11375/21621
Title: | On transverse stability of periodic waves in the Kadomtsev-Petviashvili equation |
Authors: | Li, Jin |
Advisor: | Pelinovsky, Dmitry |
Department: | Mathematics and Statistics |
Keywords: | Mathematics;Applied Mathematics |
Publication Date: | 2017 |
Abstract: | This thesis is devoted to the proof of linear stability of the one-dimensional periodic waves in the Kadomtsev-Petviashvili (KP-II) equation with respect to two-dimensional bounded perturbations. The method of the proof is based on the construction of a self-adjoint operator K such that the operators JL and JK commute, expresses a symplectic structure for the KP-II equation and L is a self-adjoint Hessian operator of the energy function at the periodic wave. In the situation when K is strictly positive except for a nite-dimensional kernel included in the kernel of L, the operator JL has no unstable eigenvalues and the associated time evolution is globally bounded. |
URI: | http://hdl.handle.net/11375/21621 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Li_Jin_201705_MSc.pdf | 366.27 kB | Adobe PDF | View/Open |
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