Related papers: Traveling wave solutions for the FPU chain: a cons…
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model…
Recent asymptotic results by the authors provided detailed information on the shape of solitary high-energy travelling waves in FPU atomic chains. In this note we use and extend the methods to understand the linearisation of the travelling…
Using the method of sub-super-solution, we construct a solution of $(-\Delta)^su-cu_z-f(u)=0$ on $\R^3$ of pyramidal shape. Here $(-\Delta)^s$ is the fractional Laplacian of sub-critical order $1/2<s<1$ and $f$ is a bistable nonlinearity.…
This paper is concerned with the traveling wave solutions for integro-difference systems of higher order. By using Schauder fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
We analyze the weak solution concept for the Fornberg-Whitham equation in case of traveling waves with a piecewise smooth profile function. The existence of discontinuous weak traveling wave solutions is shown by means of analysis of a…
We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and…
Stability of travelling waves for the Nagumo equation on the whole line is proven using a new approach via functional inequalities and an implicitely defined phase adaption. The approach can be carried over to obtain pathwise stability of…
Existence of non-negative weak solutions is shown for a full curvature thin-film model of a liquid thin film flowing down a vertical fibre. The proof is based on the application of a priori estimates derived for energy-entropy functionals.…
We investigate a model of solid propellant combustion involving surface pyrolysis coupled to finite activation energy gas phase combustion. Existence and uniqueness of a travelling wave solution are established by extending dynamical system…
We consider periodic traveling waves in FPU-type chains with superpolynomial interaction forces and derive explicit asymptotic formulas for the high-energy limit as well as bounds for the corresponding approximation error. In the proof we…
In this paper, we study the traveling wave solutions to the density-suppressed motility model describing the ``self-trapping'' mechanism that induces spatio-temporal pattern formations observed in the experiment. We establish the existence…
New travelling wave solutions to the Fornberg-Whitham equation are investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.
It is well established that the solitary waves of FPU-type chains converge in the high-energy limit to traveling waves of the hard-sphere model. In this paper we establish improved asymptotic expressions for the wave profiles as well as an…
We consider atomic chains with nearest neighbour interactions and study periodic and homoclinic travelling waves which are called wave trains and solitons, respectively. Our main result is a new existence proof which relies on the…
We derive parametric travelling-wave solutions of non-linear QCD equations. They describe the evolution towards saturation in the geometric scaling region. The method, based on an expansion in the inverse of the wave velocity, leads to a…
We examine travelling wave solutions of the Porous-Fisher model, $\partial_t u(x,t)= u(x,t)\left[1-u(x,t)\right] + \partial_x \left[u(x,t) \partial_x u(x,t)\right]$, with a Stefan-like condition at the moving front, $x=L(t)$. Travelling…
A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary…
We consider infinite FPU-type atomic chains with general convex potentials and study the existence of monotone fronts that are heteroclinic travelling waves connecting constant asymptotic states. Iooss showed that small amplitude fronts…
We discuss models for coupled wave equations describing interacting fields, focusing on the speed of travelling wave solutions. In particular, we propose a general mechanism for selecting and tuning the speed of the corresponding…