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Linear Asymptotic Stability of the Smooth 1-Solitons for the Degasperis-Procesi Equation
Simon Deng, Mathew A. Johnson, Stéphane Lafortune
In this paper, we study the asymptotic stability of smooth 1-solitons in the Degasperis-Procesi (DP) equation. Such solutions necessarily exist on a non-zero background, and their…
Modulational Instability of Small Amplitude Periodic Traveling Waves in the Novikov Equation
Brett Ehrman, Mathew A. Johnson, Stéphane Lafortune
We study the spectral stability of smooth, small-amplitude periodic traveling wave solutions of the Novikov equation, which is a Camassa-Holm type equation with cubic nonlinearitie…
Orbital Stability of Smooth Solitary Waves for the Novikov Equation
Brett Ehrman, Mathew A. Johnson, Stéphane Lafortune
We study the orbital stability of smooth solitary wave solutions of the Novikov equation, which is a Camassa-Holm type equation with cubic nonlinearities. These solitary waves are…
Orbital Stability of Periodic Traveling Waves in the -Camassa-Holm Equation
Brett Ehrman, Mathew A. Johnson
In this paper, we identify criteria that guarantees the nonlinear orbital stability of a given periodic traveling wave solution within the b-family Camassa-Holm equation. These per…