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Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation,…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means…
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…
We present a systematic derivation of relativistic lattice kinetic equations for finite-mass particles, reaching close to the zero-mass ultra-relativistic regime treated in the previous literature. Starting from an expansion of the…
We study the thermodynamics and non-relativistic hydrodynamics of the holographic fluid on a finite cutoff surface in the Gauss-Bonnet gravity. It is shown that the isentropic flow of the fluid is equivalent to a radial component of…
This study investigates unsteady boundary layer phenomena in electrically conducting fluids subjected to static magnetic fields. Using a semi-explicit similarity transformation method, the momentum equation associated with the Stokes stream…
We introduce a new heterogeneous multi-scale method for the simulation of flows of non-Newtonian fluids in general geometries and present its application to paradigmatic two-dimensional flows of polymeric fluids. Our method combines…
Initial-boundary value problem for linearized equations of motion of viscous barotropic fluid in a bounded domain is considered. Existence, uniqueness and estimates of weak solutions to this problem are derived. Convergence of the solutions…
Using Lie group theory we construct explicit solitary wave solutions of coupled nonlinear Schrodinger systems with spatially inhomogeneous nonlinearities. We present the general theory, use it to construct different families of explicit…
We introduce and study a family of lattice equations which may be viewed either as a strongly nonlinear discrete extension of the Gardner equation, or a non-convex variant of the Lotka-Volterra chain. Their deceptively simple form supports…
In this paper we give a survey on various multiscale methods for the numerical solution of second order hyperbolic equations in highly heterogeneous media. We concentrate on the wave equation and distinguish between two classes of…
This contribution presents a comprehensive overview of of lattice Boltzmann models for non-ideal fluids, covering both theoretical concepts at both kinetic and macroscopic levels and more practical discussion of numerical nature. In that…
We report the first observation of axisymmetric solitary waves on the surface of a cylindrical magnetic fluid layer surrounding a current-carrying metallic tube. According to the ratio between the magnetic and capillary forces, both…
With the rapid development of studies involving droplet microfluidics, drug delivery, cell detection, and microparticle synthesis, among others, many scientists have invested significant efforts to model the flow of these fluid-filled…
The purpose of the paper is twofold. Firstly, we want to present a Meta Theorem to show the existence of a martingale solution for coupled systems of non-linear stochastic differential equations. The idea is first to split the system by…
Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains…
We consider a system of coupled nonlinear Schr{\"o}dinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e solutions to the system with each component behaving at large times as a solitary…
Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…
We propose a new method to study motions of mixtures in fluid interfaces. We extend the equations of equilibrium in interfaces and the results associated with travelling waves for van der Waals like fluids. Maxwell rule is extended to…