Existence of Periodic Traveling Wave Solutions for a K-P-Boussinesq Type System

In this paper, via a variational approach, we show the existence of periodic traveling waves for a Kadomtsev-Petviashvili Boussinesq type system that describes the propagation of long waves in wide channels. We show that those periodic solutions are characterized as critical points of some functional, for which the existence of critical points follows as a consequence of the Mountain Pass Theorem and Arzela-Ascoli Theorem.

ON THE INSTABILITY OF PERIODIC WAVES FOR DISPERSIVE EQUATIONS—REVISITED

The purpose of this paper is to present an extension of the results in [8]. We establish a more general proof for the moving kernel formula to prove the spectral stability of periodic traveling wave solutions for the regularized Benjamin–Bona–Mahony type equations. As applications of our analysis, we show the spectral instability for the quintic Benjamin–Bona–Mahony equation and the spectral (orbital) stability for the regularized Benjamin–Ono equation.

High-Frequency Instabilities of a Boussinesq–Whitham System: A Perturbative Approach

We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of a Boussinesq–Whitham system. These solutions are shown numerically to exhibit high-frequency instabilities when subject to bounded perturbations on the real line. We use a formal perturbation method to estimate the asymptotic behavior of these instabilities in the small-amplitude regime. We compare these asymptotic results with direct numerical computations.

Waves of maximal height for a class of nonlocal equations with inhomogeneous symbols

In this paper, we consider a class of nonlocal equations where the convolution kernel is given by a Bessel potential symbol of order α for α > 1. Based on the properties of the convolution operator, we apply a global bifurcation technique to show the existence of a highest, even, 2 π-periodic traveling-wave solution. The regularity of this wave is proved to be exactly Lipschitz.

Spreading speed and periodic traveling waves of a time periodic and diffusive SI epidemic model with demographic structure

<p style='text-indent:20px;'>We study the asymptotic spreading properties and periodic traveling wave solutions of a time periodic and diffusive SI epidemic model with demographic structure (follows the logistic growth). Since the comparison principle is not applicable to the full system, we analyze the asymptotic spreading phenomena for susceptible class and infectious class by comparing with respective relevant periodic equations with KPP-type. By applying fixed point theorem to a truncated problem on a finite interval, combining with limit idea, the existence of periodic traveling wave solutions are derived. The results show that the minimal wave speed exactly equals to the spreading speed of infectious class when susceptible class is abundant.</p>

Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV Equations

In this paper, by applying the Jacobian ellipse function method, we obtain a group of periodic traveling wave solution of coupled KdV equations. Furthermore, by the implicit function theorem, the relation between some wave velocity and the solution’s period is researched. Lastly, we show that this type of solution is orbitally stable by periodic perturbations of the same wavelength as the underlying wave.