Related papers: Kinks and solitons in linear and nonlinear-diffusi…
An impact of kink-type solitons on infrared lattice vibrations is studied for incommensurate Frenkel-Kontorova model. It is shown that the vibration of particles involved into the kink formation is very similar to that in a gap mode around…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
Nonlinear effects in the propagation of perturbations in a dusty electron-ion plasma is studied, considering fully relativistic wave motion. A multifluid model is considered for the particles, from which a KdV equation can be derived. In…
In this paper we study the initial boundary value problem for the system $u_t-\Delta u^m=-\mbox{div}(u^{q}\nabla v),\ v_t-\Delta v+v=u$. This problem is the so-called Keller-Segel model with nonlinear diffusion. Our investigation reveals…
We show how to obtain general nonlinear aggregation-diffusion models, including Keller-Segel type models with nonlinear diffusions, as relaxations from nonlocal compressible Euler-type hydrodynamic systems via the relative entropy method.…
The propagation of heat and thermal signals in the form of travelling waves is investigated for a nonlinear Maxwell-Cattaneo-Vernotte equation. The exact wave solutions are derived by expressing the thermal conductivity and the relaxation…
We study the behavior of the soliton which, while moving in non-dissipative medium encounters a barrier with finite dissipation. The modelling included the case of a finite dissipative layer similar to a wave passing through the…
We study the existence of steady states to the Keller-Segel system with linear chemotactical sensitivity function on a smooth bounded domain in $\mathbb R^N,$ $N\ge3,$ having rotational symmetry. We find three different types of…
In this paper, by using bifurcation method, we successfully find the Fornberg-Whitham equation has a type of traveling wave solutions called kink-like wave solutions and antikinklike wave solutions. They are defined on some semifinal…
Transversal oscillations of spicules axes may be related to the propagation of magnetohydrodynamic waves along them. These waves may become unstable and the instability can be of the Kelvin-Helmholtz type. We use the dispersion relation of…
The problem of stability and spectrum of linear excitations of a soliton (kink) of the dispersive sine-Gordon and $\varphi^4$ - equations is solved exactly. It is shown that the total spectrum consists of a discrete set of frequencies of…
All solutions of the Korteweg -- de Vries equation that are bounded on the real line are physically relevant, depending on the application area of interest. Usually, both analytical and numerical approaches consider solution profiles that…
In this paper, we study the existence of traveling wave solutions and the spreading speed for the solutions of an age-structured epidemic model with nonlocal diffusion. Our proofs make use of the comparison principles both to construct…
This work describes a hyperbolic model for cell-cell repulsion with population dynamics. We consider the pressure produced by a population of cells to describe their motion. We assume that cells try to avoid crowded areas and prefer locally…
We first show the existence of unique global minimizer of the free energy for all masses associated to a nonlinear diffusion version of the classical Keller-Segel model when the diffusion dominates over the attractive force of the…
We study light propagation in waveguide arrays made in Kerr nonlinear media with a transverse refractive index gradient, and we find that the presence of the refractive index gradient leads to the appearance of a number of new soliton…
This paper is concerned with non-cooperative parabolic reaction--diffusion systems which share structural similarities with the scalar Fisher--KPP equation. In a previous paper, we established that these systems admit traveling wave…
In traffic flow, self-organized wave propagation, which characterizes congestion, has been reproduced in macroscopic and microscopic models. Hydrodynamic models, a subset of macroscopic models, can be derived from microscopic-level…
A new type of wave-mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a…
Optical propagation and vortices in nonlinear media have been intensively studied in modern optical physics. In this paper, we establish constraints regarding the propagation constant and provide an existence theory and numerical…