5 papers
Orbital Stability of Smooth Traveling Solitary Waves to the Fornberg-Whitham Equation
Xijun Deng, Stephane Lafortune, Zhisu Liu
The Fornberg-Whitham (FW) equation was introduced by Fornberg and Whitham [Fornberg and Whitham, Phil. Trans. R. Soc. Lond. A (1978)] as a nonlocal model for unidirectional shallow…
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…
Orbital stability of smooth solitary waves for the modified Camassa-Holm equation
Xijun Deng, Stéphane Lafortune, Zhisu Liu
In this paper, we explore the orbital stability of smooth solitary wave solutions to the modified Camassa-Holm equation with cubic nonlinearity. These solutions, which exist on a n…
Stability of 2-soliton solutions for the modified Camassa-Holm equation with cubic nonlinearity
Xijun Deng, Stéphane Lafortune, Zhisu Liu
In this paper, we are concerned with the stability of 2-soliton solutions on a nonzero constant background for the modified Camassa-Holm equation with cubic nonlinearity. By employ…
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…