Periodic traveling wavesSingular perturbationsIn this paper we will consider a predator–prey model with a non-constant death rate and distributed delay, described by a partial integro-differential system. The main goal of this work is to prove that the partial integro-differential system has ...
An exact wave-action equation is introduced if the traveling wave is stable, involving averages over the periodic wave as well as time. This is equivalent to an extended averaged Lagrangian principle. The equation for the slow modulations of the phase shift of the traveling wave is derived ...
Studies in Applied MathematicsR. Haberman. Phase shift modulations for stable, oscillatory, traveling, strongly nonlinear waves. Stud. Appl. Math. , 84(1):57–69, 1991. MATH MathSciNetHaberman, R. (1991) Phase shift modulations for stable, oscillatory, traveling, strongly nonlinear waves. ...
mono-stable reaction-diffusion equationsThis paper is concerned with planar traveling wavefronts of mono-stable reaction-diffusion equations in R-n (n >= 2). We show that the large time behavior of the disturbed fronts can be controlled by two functions, which are the solutions of the ...
Reitich, Stable, high-order computation of traveling water waves in three dimensions, Eur. Jour. Mech. B/ Fluids, 25, 406-424, 2006.D.P. Nicholls, F. Reitich, Rapid, stable, high-order computation of traveling water waves in three dimensions, Eur. J. Mech. B Fluids 25 (4) (2006...
Using the Lotka-Volterra competition model as an example, a method is developed for determining this minimum wave speed. In the example model, the exact minimum wave speed is determined. Furthermore, the method could be applied to other models. A related problem is the question of uniqueness....