Related papers: Traveling waves for SIR model on two-dimensional l…
We find a new class of solutions that are traveling waves on the boundary of two--dimensional droplet of ideal fluid. We assume that the free surface is subject only to the force of surface tension, and the fluid flow is potential. We use…
In this paper we study existence and asymptotic behavior of solitary-wave solutions for the generalized Shrira equation, a two-dimensional model appearing in shear flows. The method used to show the existence of such special solutions is…
Some classes of the so called "travelling wave" solutions of Einstein and Einstein - Maxwell equations in General Relativity and of dynamical equations for massless bosonic fields in string gravity in four and higher dimensions are…
The traveling waves for surface diffusion of plane curves are studied. We consider an evolving plane curve with two endpoints, which can move freely on the x-axis with generating constant contact angles. For the evolution of this plane…
In this study, we analyze the behavior of monotone traveling waves of a one-dimensional porous medium equation modeling mechanical properties of living tissues. We are interested in the asymptotics where the pressure, which governs the…
In 1992 G. B. Ermentrout and J. B. McLeod published a landmark study of traveling wave fronts for a differential-integral equation modeling a neural network. Since then a number of authors have extended the model by adding an additional…
In this work we revisit the existence, stability and dynamics of unstable traveling solitary waves in the context of lattice dynamical systems. We consider a nonlinear lattice of an $\alpha$-Fermi-Pasta-Ulam type with the additional feature…
We establish several existence results for traveling-wave solutions of the nonlocal derivative nonlinear Schr\"odinger equation with general coefficients by variational methods. We study associated minimization problems in the subcritical…
We show the existence of periodic traveling waves at the free surface of a two dimensional, infinitely deep, and constant vorticity flow, under gravity, whose profiles are overhanging, including one which intersects itself to enclose a…
We consider a single component reaction-diffusion equation in one dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. Our main result shows the existence, uniqueness (up to…
We study the existence of traveling waves of reaction-diffusion systems with delays in both diffusion and reaction terms of the form $\partial u(x,t)/\partial t = \Delta u(x,t-\tau_1)+f(u(x,t),u(x,t-\tau_2))$, where $\tau_1,\tau_2$ are…
This survey covers the mathematical theory of steady water waves with an emphasis on topics that are at the forefront of current research. These areas include: variational characterizations of traveling water waves; analytical and numerical…
In this paper, we present a complete classification of traveling wave solutions for monostable systems within a unified framework. To this end, we introduce a novel technique, referred to as the slicing method, which is based on the…
We present in closed form some special travelling-wave solutions (on the real line or on the circle) of a perturbed sine-Gordon equation. The perturbation of the equation consists of a constant forcing term $\gamma$ and a linear dissipative…
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 introduce a two-dimensional Hele-Shaw type free boundary model for motility of eukaryotic cells on substrates. The key ingredients of this model are the Darcy law for overdamped motion of the cytoskeleton gel (active gel) coupled with…
In this paper we mainly investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed. We assume that the free surface is almost periodic in the horizontal direction. Using…
We prove the existence of solitary waves in a lattice where all particles interact with each other by pair-wise repulsive forces that decay with distance. The variational existence proof is based on constrained optimization and provides a…
In the framework of hyperbolic conservation laws regularised by including diffusive and dispersive terms, we study monotone travelling waves for the generalised Rosenau-Korteweg de Vries equation. We establish existence as well as linear…
We study a non-linear and non-local evolution equation for curves obtained as the sharp interface limit of a phase-field model for crawling motion of eukaryotic cells on a substrate. We establish uniqueness of solutions to the sharp…