相关论文: Existence of traveling waves for vector valued gra…

We use a simple method that leads to the integrals involved in obtaining the traveling wave solutions of wave equations with one and two exponential nonlinearities. When the constant term in the integrand is zero, implicit solutions in…

We prove that traveling waves in viscous compressible liquids are a generic phenomenon. The setting for our result is a horizontally infinite, finite depth layer of compressible, barotropic, viscous fluid, modeled by the free boundary…

The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence…

In this paper we prove a local-in-time existence theorem for an initial-boundary value problem related to a model of temperature-dependent phase segregation that generalizes the standard Allen-Cahn's model. The problem is ruled by a system…

In this paper, we consider bounded positive solutions to the Allen-Cahn equation on complete noncompact Riemannian manifolds without boundary. We derive gradient estimates for those solutions. As an application, we get a Liouville type…

We show that the combined action of diffraction and convection (walk-off) in wave mixing processes leads to a nonlinear-symmetry-breaking in the generated traveling waves. The dynamics near to threshold is reduced to a Ginzburg-Landau…

We prove existence results for travelling waves in discrete, damped, dc-driven sine-Gordon equations with periodic boundary conditions.

The $\mathcal{C}^{\infty}$-structure-based method of integration of distributions of vector fields is used to classify all the traveling wave solutions of the modified Zakharov--Kuznetsov equation. This work unifies and generalizes the…

In the seminal work of Benjamin,\cite{Ben} in the late 70's, he has derived the ubiquitous Benjamin model, which is a reduced model in the theory of water waves. Notably, it contains two parameters in its dispersion part and under some…

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…

This paper presents a conditional convergence result of solutions to the Allen--Cahn equation with arbitrary potentials to a De Giorgi type $ \mathrm{BV} $-solution to multiphase mean curvature flow. Moreover we show that De Giorgi type…

In this paper we study existence of traveling waves for 1-D compressible Euler system with dispersion (which models quantum effects through the Bohm potential) and nonlinear viscosity in the context of quantum hydrodynamic models for…

The main topic of this paper is the analysis and modeling of stop-and-go waves, observable in experiments of single lane movement with pedestrians. The velocity density relation using measurements on a 'microscopic' scale shows the…

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…

Nonlinear wave phenomena such as stop-and-go traffic patterns are widely observed in vehicular flow but remain challenging to describe within a rigorous mathematical framework. Motivated by this, we investigate nonlinear wave structures in…

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 consider high frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism…

For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation…

Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to a universal…

We examine the possibility of travelling wave solutions within the nonlinear Euler-Heisenberg electrodynamics. Since this theory resembles in its form the electrodynamics in matter, it is a priori not clear if there exist travelling wave…