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Please use this identifier to cite or link to this item: http://hdl.handle.net/11375/26805
Title: Existence and Stability of Periodic Waves in the Fractional Korteweg-de Vries Type Equations
Authors: Le, Uyen
Advisor: Pelinovsky, Dmitry
Department: Mathematics
Keywords: Fractional Korteweg-de Vries equation, fractional modified Korteweg-de Vries equation, Petviashvili method, Green's function of fractional Laplacian operator, periodic travelling waves, existence, spectral stability, bifurcation, energy minimization
Publication Date: 2021
Abstract: 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.
URI: http://hdl.handle.net/11375/26805
Appears in Collections:Open Access Dissertations and Theses

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