Related papers: Index theory for traveling waves in reaction diffu…
This paper is concerned with the existence of traveling wave solutions for diffusive two-species Lotka-Volterra systems with delay in both the reaction and diffusion terms without monotonicity. We extend the partial or cross monotone…
We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invariant under translations. In the deterministic setting,…
We derive the Whitham modulation equations for the Zakharov-Kuznetsov equation via a multiple scales expansion and averaging two conservation laws over one oscillation period of its periodic traveling wave solutions. We then use the Whitham…
This work derives the Navier--Stokes hydrodynamic equations for a model of a confined, quasi-two-dimensional, $s$-component mixture of inelastic, smooth, hard spheres. Using the inelastic version of the revised Enskog theory, macroscopic…
Linearization around unstable travelling waves in excitable systems can be used to approximate strength-extent curves in the problem of initiation of excitation waves for a family of spatially confined perturbations to the rest state. This…
We study a reaction-diffusion system of partial differential equations, which can be taken to be a basic model for criminal activity. We show that the assumption of a populations natural tendency towards crime significantly changes the…
Spectrograms provide an efficient way to analyse surface elevation signals of ship waves taken from a sensor fixed at a single point in space. Recent work based on a simplified model for the ship's disturbance suggests that matching the…
It is well-known that the existence of traveling wave solutions for reaction-diffusion partial differential equations can be proved by showing the existence of certain heteroclinic orbits for related autonomous planar differential…
The present paper is devoted to the study of stability, uniqueness and recurrence of generalized traveling waves of reaction-diffusion equations in time heterogeneous media of ignition type, whose existence has been proven by the authors of…
The purpose of this work is to introduce a concept of traveling waves in the setting of periodic metric graphs. It is known that the nonlinear Schr{\"o}dinger (NLS) equation on periodic metric graphs can be reduced asymptotically on long…
A thorough analysis is performed to find traveling waves in a qualitative reaction-diffusion system inspired by a predator-prey model. We provide rigorous results coming from a standard local stability analysis, numerical bifurcation…
A nonlinear PDE featuring flux limitation effects together with those of the porous media equation (nonlinear Fokker-Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and…
The Penrose-Fife Phase Field Model is now a well-established model in the theory of phase transitions. In the course of study of this model both the rigorous mathematical results and approximate solutions were obtained. However, to the best…
In order to find an approximate solution to the Vlasov-Maxwell equation system describing the lower hybrid wave propagation in magnetic confined plasmas, the use of the WKB method leads to the ray tracing equations. The Hamiltonian…
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…
A wave equation, that governs finite amplitude acoustic disturbances in a thermoviscous Newtonian fluid, and includes nonlinear terms up to second order, is proposed. In contrast to the model known as the Kuznetsov equation, the proposed…
In this review, we provide a concise summary of several important mathematical results for stochastic travelling waves generated by monostable and bistable reaction-diffusion stochastic partial differential equations (SPDEs). In particular,…
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…
First, we make a revision of the up-to-date Passive Scalar Fields properties: also, the refractive index is among them. Afterwards, we formulated the properties that make the family of `isotropic' fractional Brownian motion (with parameter…
In the present work, we revisit the so-called regularized short pulse equation (RSPE) and, in particular, explore the traveling wave solutions of this model. We theoretically analyze and numerically evolve two sets of such solutions. First,…