Related papers: The Modultional Instability for a Generalized KdV …
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…
We study stability of solitary wave solutions for the fractional generalized Korteweg-de Vries equation $$ \partial_t u- \partial_{x_1} D^{\alpha}u+ \tfrac{1}{m}\partial_{x_1}(u^m)=0, ~ (x_1,\dots,x_d)\in \mathbb{R}^d, \, \, t\in…
In this paper, it is proved that the KdV-Burgers equation with a monostable source term of Fisher-KPP type has small-amplitude periodic traveling wave solutions with finite fundamental period. These solutions emerge from a subcritical local…
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
We consider the logarithmic Korteweg-de Vries (log-KdV) equation, which models solitary waves in anharmonic chains with Hertzian interaction forces. By using an approximating sequence of global solutions of the regularized generalized KdV…
We study general semilinear scalar-field equations on the real line with variable coefficients in the linear terms. These coefficients are uniformly small, but slowly decaying, perturbations of a constant-coefficient operator. We are…
In this paper, we investigate the instability of one-dimensionally stable periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbations in the generalized Zakharov-Kuznetsov…
The generalized nonlinear Schr\"odinger equation with full dispersion (FDNLS) is considered in the semiclassical regime. The Whitham modulation equations are obtained for the FDNLS equation with general linear dispersion and a generalized,…
We study the modulational instability of small-amplitude periodic traveling wave solutions in a dispersion generalized Ostrovsky equation. Specifically, we investigate the invertibility of the associated linearized operator in the vicinity…
We study the modulational instability of smooth, small-amplitude periodic traveling wave solutions to the $b$-family of Novikov equation with cubic nonlinearity with an arbitrary coefficient $b>0$. Our approach is based on applying spectral…
Global and local absolute instabilities of 2D wakes are known to be stabilized by spanwise periodic modulations of the wake profile. The present study shows that this stabilizing effect is of general nature and can be mimicked by enforcing…
In this paper, we investigate the spectral stability of periodic traveling waves for a cubic-quintic and double dispersion equation. Using the quadrature method we find explict periodic waves and we also present a characterization for all…
We determine the stability and instability of a sufficiently small and periodic traveling wave to long wavelength perturbations, for a nonlinear dispersive equation which extends a Camassa-Holm equation to include all the dispersion of…
This paper focuses on the modulation instability, conservation laws and localized wave solutions of the generalized coupled Fokas-Lenells equation. Based on the theory of linear stability analysis, distribution pattern of modulation…
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…
We consider the nonlinear wave modulation of arbitrary amplitude periodic traveling wave solutions of the Ostrovsky equation, which arises as a model for the unidirectional propagation of small-amplitude, weakly nonlinear surface and…
This paper studies both existence and spectral stability properties of bounded spatially periodic traveling wave solutions to a large class of scalar viscous balance laws in one space dimension with a reaction function of monostable or…
We consider the periodic standing waves in the derivative nonlinear Schrodinger (DNLS) equation arising in plasma physics. By using a newly developed algebraic method with two eigenvalues, we classify all periodic standing waves in terms of…
We address the count of isolated and embedded eigenvalues in a generalized eigenvalue problem defined by two self-adjoint operators with a positive essential spectrum and a finite number of isolated eigenvalues. The generalized eigenvalue…
Various approaches to studying the stability of solutions of nonlinear PDEs lead to explicit formulae determining the stability or instability of the wave for a wide range of classes of equations. However, these are typically specialized to…