This thesis is concerned with the existence and spectral stability of periodic
waves in the fractional Korteweg-de Vries (KdV) equation and the fractional
modified Korteweg-de Vries (mKdV) equation. We study the existence of
periodic travelling waves using various tools such as Green's function for fractional
Laplacian operator, Petviashvili fixed point method, and a new variational
characterization in which the periodic waves in fractional KdV and
fractional mKdV are realized as the constrained minimizers of the quadratic
part of the energy functional subject to fixed L3 and L4 norm respectively.
This new variational framework allows us to identify the existence region of
periodic travelling waves and to derive the criterion for spectral stability of
the periodic waves with respect to perturbations of the same period. / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/26805 |
| Date | January 2021 |
| Creators | Le, Uyen |
| Contributors | Pelinovsky, Dmitry, Mathematics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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