相关论文: Traveling wave solutions for the FPU chain: a cons…

For the one-dimensional case, we establish the long-time asymptotics of solution to Cauchy problem and prove existence of modified wave operators. In particular, we show that the part of the wave travels ballistically if the potential is…

This paper reports results on the classification of traveling wave solutions, including nonnegative weak sense, in the spatial 1D degenerate parabolic equation. These are obtained through dynamical systems theory and geometric approaches…

Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…

This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…

We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…

In this paper, we present a computer-assisted approach for constructively proving the existence of traveling wave solutions of the suspension bridge equation on the infinite strip $\Omega = \mathbb{R} \times (-d_2,d_2)$. Using a meticulous…

Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at Re = 2000 in a saddle-node infinite period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks…

In this paper, we investigate the instability of the spherical travelling wave solutions for the Transport-Stokes system in $\mathbb{R}^3$. First, a classical scaling argument ensures instability among all probability measures for the…

We give an exhaustive characterization of singular weak solutions for ordinary differential equations of the form $\ddot{u}\,u + \frac{1}{2}\dot{u}^2 + F'(u) =0$, where $F$ is an analytic function. Our motivation stems from the fact that in…

This paper is concerned with the traveling waves of delayed reaction-diffusion systems where the reaction function possesses the mixed quasimonotonicity property. By the so-called monotone iteration scheme and Schauder's fixed point…

In this study, we investigate the existence of traveling wave solutions for a SIR model on two-dimensional lattice. The existence of traveling waves is established within the framework of upper and lower solutions and the Schauder…

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…

We give sufficient conditions for the existence of positive travelling wave solutions for multi-dimensional autonomous reaction-diffusion systems with distributed delay. To prove the existence of travelling waves, we give an abstract…

We prove the existence of a traveling wave solution for a boundary reaction diffusion equation when the reaction term is the combustion nonlinearity with ignition temperature. A key role in the proof is plaid by an explicit formula for…

We consider the one-dimensional KPP-equation driven by space-time white noise and extend the construction of travelling wave solutions arising from Heavyside initial data from [Tribe, 1996, MR1396765] to non-negative continuous functions…

In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as Mass-in-Mass systems. We use 3 distinct approaches to identify relevant traveling waves. The first consists of…

The purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the Gross-Pitaevskii equation in dimensions two and three. Our arguments, based on minimization under constraints, yield…

We investigate a new class of topological travelling-wave solutions for a macroscopipc swarmalator model involving force non-reciprocity. Swarmalators are systems of self-propelled particles endowed with a phase variable. The particles are…

In this paper, we construct the transport equation and the wave equation with specular derivatives and solve these equations in one-dimension. To solve these equations, we introduce new function spaces, which we term specular spaces,…

In this article, we provide an alternative way to construct small amplitude traveling waves for general Whitham type equations, in both periodic and whole line contexts. More specifically, Fourier analysis techniques allow us to reformulate…