Related papers: Stability of multi antipeakon-peakons profile
In this paper, we study the Cauchy problem for a generalized cross-coupled Camassa-Holm system with peakons and higher-order nonlinearities. By the transport equation theory and the classical Friedrichs regularization method, we obtain the…
We numerically investigate transverse stability and instability of so-called cnoidal waves, i.e., periodic traveling wave solutions of the Korteweg-de Vries equation, under the time-evolution of the Kadomtsev-Petviashvili equation. In…
This paper has various goals: first, we develop a local and global well-posedness theory for the regularized Benjamin-Ono equation in the periodic setting, second, we show that the Cauchy problem for this equation (in both periodic and…
In this paper we show that non-smooth functions which are distributional traveling wave solutions to the two component Camassa-Holm equation are distributional traveling wave solutions to the Camassa-Holm equation provided that the set…
We prove that the peakons are asymptotically H 1-stable, under the flow of the Degasperis-Procesi equation, in the class of functions with a momentum density that belongs to M + (R). The key argument is a rigidity result for uniformly in…
We study the existence and orbital stability/instability of periodic standing wave solutions for the Klein-Gordon-Schr\"odinger system with Yukawa and cubic interactions. We prove the existence of periodic waves depending on the Jacobian…
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg--de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for…
In the seminal work of Benjamin,\cite{Ben} in the late 70's, he has derived the ubiquitous Benjamin model, which is a reduced model in the theory of water waves. Notably, it contains two parameters in its dispersion part and under some…
In this paper, we consider the following nonlinear Klein-Gordon equation \begin{align*} \partial_{tt}u-\Delta u+u=|u|^{p-1}u,\qquad t\in \mathbb{R},\ x\in \mathbb{R}^d, \end{align*} with $1<p< 1+\frac{4}{d}$. The equation has the standing…
In previous works [4, 5], existence and uniqueness of travelling waves for the nonlinear Schr\"odinger equations have been shown for speeds close to the speed of sound. Furthermore, it has been proved that a chain of dark solitons of…
We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all…
In this paper, we present the first result concerning the orbital stability of periodic traveling waves for the modified Kawahara equation. Our method is based on the Fourier expansion of the periodic wave in order to know the behaviour of…
We study the spectral stability properties of periodic traveling waves in the sine-Gordon equation, including waves of both subluminal and superluminal propagation velocities as well as waves of both librational and rotational types. We…
The modified Camassa-Holm equation (also called FORQ) is one of numerous $cousins$ of the Camassa-Holm equation possessing non-smoth solitons ($peakons$) as special solutions. The peakon sector of solutions is not uniquely defined: in one…
Long-time evolution of a weakly perturbed wavetrain near the modulational instability threshold is investigated within the framework of the compact Zakharov equation for unidirectional deep-water waves, recently derived by Zakharov &…
The KP-II equation was derived by Kadmotsev and Petviashvili to explain stability of line solitary waves of shallow water. Recently, Mizumachi (Mem. Amer. Math. Soc. 238 (2015)) has proved nonlinear stability of $1$-line solitons for…
The stability of periodic traveling wave solutions to dispersive PDEs with respect to `arbitrary' perturbations is still widely open. The focus is put here on stability with respect to perturbations of the same period as the wave, for…
In this article, we focus on the stability of dark solitons for a general one-dimensional nonlinear Schr\"odinger equation. More precisely, we prove the orbital stability of a chain of travelling waves whose speeds are well ordered, taken…
The pentaquark is studied in a simple model of confinement where the quarks and the antiquark are linked by flux tubes of minimal cumulated length, and the Coulomb-like interaction, the spin-dependent terms and the antisymmetrization…
The Degasperis-Procesi (DP) equation is an integrable Camassa-Holm-type model as an asymptotic approximation for the unidirectional propagation of shallow water waves. This work is to establish the $L^2\cap L^\infty$ orbital stability of a…