40 citations · 49 across the 11 of their papers we have counts for
11 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…
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…
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…
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…
Spectral instability of peakons for the -family of Novikov equations
Xijun Deng, Stéphane Lafortune
In this paper, we are concerned with a one-parameter family of peakon equations with cubic nonlinearity parametrized by a parameter usually denoted by the letter . This family i…
Stability of fronts in the diffusive Rosenzweig-MacArthur model
Anna Ghazaryan, Stéphane Lafortune, Yuri Latushkin +1
We consider a diffusive Rosenzweig-MacArthur predator-prey model in the situation when the prey diffuses at the rate much smaller than that of the predator. In a certain parameter…
Discrete systems related to some equations of the Painlevé-Gambier classification
S. Lafortune, B. Grammaticos, A. Ramani +1
We derive integrable discrete systems which are contiguity relations of two equations in the Painlevé-Gambier classification depending on some parameter. These studies extend earli…
Discrete and Continuous Linearizable Equations
S. Lafortune, B. Grammaticos, A. Ramani
We study the projective systems in both continuous and discrete settings. These systems are linearizable by construction and thus, obviously, integrable. We show that in the contin…
The Gambier Mapping, Revisited
B. Grammaticos, A. Ramani, S. Lafortune
We examine critically the Gambier equation and show that it is the generic linearisable equation containing, as reductions, all the second-order equations which are integrable thro…