Related papers: New exact travelling wave solutions for the K(2,2)…
This paper deals with the exact solutions of a nonlinear coupled coupled wave equation. The (G'/G)-expansion method has been applied to derive kink solutions and singular wave solutions. The restrictions on the coefficients of the governing…
A potential dynamics approach is developed to determine the periodic standing and traveling wave patterns associated with self-propelling camphor objects floating on ring-shaped water channels. Exact solutions of the wave patterns are…
Solitary waves are localized gravity waves that preserve their consistency and henceforth their visibility through properties of nonlinear hydrodynamics. Solitary waves have finite amplitude and spread with constant speed and constant…
We consider the quartic focusing Half Wave equation (HW) in one space dimension. We show first that that there exist traveling wave solutions with arbitrary small $H^{\frac 12}(\R)$ norm. This fact shows that small data scattering is not…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
In this paper we show that non-smooth functions which are distributional traveling wave solutions to the two component Camassa-Holm equation are distributional traveling wave solutions to the Camassa-Holm equation provided that the set…
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…
We study travelling wave solutions of a 1D continuum model for collective cell migration in which cells are characterised by position and polarity. Four different types of travelling wave solutions are identified which represent…
We review recent advances regarding the long-time dynamics of space-periodic water waves, focusing on 1) bifurcation of quasi-periodic solutions, both standing and traveling; 2) long-time well-posedness results; 3) modulational instability…
Stability of the traveling wave solution to a general class of one-dimensional nonlocal evolution equations is studied in $L^2$-spaces, thereby providing an alternative approach to the usual spectral analysis with respect to the supremum…
We study linear stability of planar travelling waves for a scalar reaction-diffusion equation with non-linear anisotropic diffusion. The mathematical model is derived from the full thermo-hydrodynamical model describing the process of…
Stability of a set of travelling wave solutions to the hyperbolic generalization of the convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.
We obtain exact travelling wave solutions for three families of stochastic one-dimensional nonequilibrium lattice models with open boundaries. These solutions describe the diffusive motion and microscopic structure of (i) of shocks in the…
The contribution of the "rapid" part of the pressure diffusion to the turbulent kinetic energy balance is analyzed, and a new model to describe its effect is suggested. A new transport equation for the turbulent kinetic energy is derived.…
We prove a principle of linearized stability for traveling wave solutions to neural field equations posed on the real line. Additionally, we provide the existence of a finite dimensional invariant center manifold close to a traveling wave,…
A key feature of $(1+1)$-dimensional nonlinear wave equations is that they admit left or right traveling waves, under appropriate algebraic conditions on the nonlinearities. In this paper, we prove global stability of such traveling wave…
The propagation of ON-OFF signals with dispersive waves is examined in this study. An integral-form exact solution for a simple ON-OFF switching event is derived, which holds for any dispersion relation. The integral can be exactly…
This paper is concerned with the existence and the stability of travelling wave solutions to a bistable reaction-diffusion equation with a jump discontinuious point on nonlinear term. Sub-super solution method is used throughout this paper.…
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 1967, Whitham proposed a simplified surface water-wave model which combined the full linear dispersion relation of the full Euler equations with a weakly linear approximation. The equation he postulated which is now called the Whitham…