Traveling wave solutions of Burgers equation for power-law non-Newtonian flows.
Traveling wave solutions of the heat flow of director fields
Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity: some results and open problems
This text is a survey of recent results on traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity. We present the existence, nonexistence and stability results and we describe the main ideas used in proofs.
Traveling waves in a cylinder rolling on a flat surface
Traveling waves in a one-dimensional heterogeneous medium
Traveling waves with paraboloid like interfaces for balanced bistable dynamics
Travelling fronts in cylinders
Travelling graphs for the forced mean curvature motion in an arbitrary space dimension
We construct travelling wave graphs of the form , , , solutions to the -dimensional forced mean curvature motion () with prescribed asymptotics. For any -homogeneous function , viscosity solution to the eikonal equation , we exhibit a smooth concave solution to the forced mean curvature motion whose asymptotics is driven by . We also describe in terms of a probability measure on .
Travelling wave analysis of an isothermal Euler-Poisson model
Travelling wave for absorption-convection-diffusion equations.
Travelling wave solutions for the KdV-Burgers-Kuramoto and nonlinear Schrödinger equations which describe pseudospherical surfaces.
Travelling wave solutions for the Painlevé-integrable coupled KdV equations.
Travelling wave solutions to some PDEs of mathematical physics.
Travelling waves for a certain first-order coupled PDE system.
Travelling waves for a neural network.
Travelling waves for gas-solid reactions.
Bounded traveling waves, arising in combustion model for gas-solid reactions in a porous medium, are studied. We consider the existence, uniqueness and several qualitative properties. In particular we investigate waves with finiteness and derive estimates in the limit of vanishing diffusion.
Travelling waves for the Gross-Pitaevskii equation I
Travelling Waves in Near-Degenerate Bistable Competition Models
We study a class of bistable reaction-diffusion systems used to model two competing species. Systems in this class possess two uniform stable steady states representing semi-trivial solutions. Principally, we are interested in the case where the ratio of the diffusion coefficients is small, i.e. in the near-degenerate case. First, limiting arguments are presented to relate solutions to such systems to those of the degenerate case where one species...
Travelling Waves in Partially Degenerate Reaction-Diffusion Systems
We study the existence and some properties of travelling waves in partially degenerate reaction-diffusion systems. Such systems may for example describe intracellular calcium dynamics in the presence of immobile buffers. In order to prove the wave existence, we first consider the non degenerate case and then pass to the limit as some of the diffusion coefficient converge to zero. The passage to the limit is based on a priori estimates of solutions independent of the values of the diffusion coefficients....
Travelling waves in the lattice epidemic model.