相关论文: Orbital stability of periodic traveling-wave solut…
This paper establishes suficient conditions for the orbital stability of one-parameter spatially periodic traveling-wave solutions for one-dimensional dispersive equations. Our method of proof combines known techniques with some new ideas.…
In this paper we establish the orbital stability of periodic traveling waves for a general class of dispersive equations. We use the Implicit Function Theorem to guarantee the existence of smooth solutions depending of the corresponding…
In this paper, we establish a new criterion for the orbital stability of periodic waves related to a general class of regularized dispersive equations. More specifically, we present sufficient conditions for the stability without knowing…
The present paper deals with sufficient conditions for orbital stability of periodic waves of a general class of evolution equations supporting nonlinear dispersive waves. Our method can be seen as an extension to spatially periodic waves…
In this paper, we study the orbital stability for a four-parameter family of periodic stationary traveling wave solutions to the generalized Korteweg-de Vries equation. In particular, we derive sufficient conditions for such a solution to…
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…
New results concerning the orbital stability of periodic traveling wave solutions for the "abcd" Boussinesq model will be shown in this manuscript. For the existence of solutions, we use basic tools of ordinary differential equations to…
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 periodic waves exist as 3-parameter families (up to spatial…
Recently, the Whitham and capillary-Whitham equations were shown to accurately model the evolution of surface waves on shallow water. In order to gain a deeper understanding of these equations, we compute periodic, traveling-wave solutions…
In this paper, we investigate the existence and spectral stability of periodic traveling wave solutions for the regularized Camassa-Holm equation. To establish the existence of periodic waves, we employ tools from bifurcation theory to…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
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…
In this paper we establish the orbital stability of periodic waves related to the logarithmic Korteweg-de Vries equation. Our motivation is inspired in the recent work \cite{carles}, in which the authors established the well-posedness and…
The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its…
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…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
This paper deals with the existence of travelling wave solutions for a general one-dimensional nonlinear Schr\"odinger equation. We construct these solutions by minimizing the energy under the constraint of fixed momentum. We also prove…
This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small-amplitude waves with small enough vortex strength are conditionally…
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…
We study the existence and stability of periodic traveling-wave solutions for the quadratic and cubic nonlinear Schr\"odinger equations in one space dimension.