Related papers: Modified dispersionless Veselov--Novikov equations…
A framework for defining stochastic currents associated with diffusion processes on curved Riemannian manifolds is presented. This is achieved by introducing an overdamped Stratonovich-Langevin equation that remains fully covariant under…
Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…
Systems of hydrodynamic type equations derived from the Navier-Stokes equations and the boundary layer equations are considered. A transformation of the Crocco type reducing the equation order for the longitudinal velocity component is…
Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile,…
We develop a hydrodynamic description of the classical Calogero-Sutherland liquid: a Calogero-Sutherland model with an infinite number of particles and a non-vanishing density of particles. The hydrodynamic equations, being written for the…
We study the following family of evolutionary 1+1 PDEs that describe the balance between convection and stretching for small viscosity in the dynamics of 1D nonlinear waves in fluids: \[ m_t + \underbrace{um_x \}…
In the paper a new nonlinear equation describing shallow water waves with the topography of the bottom directly taken into account is derived. This equation is valid in the weakly nonlinear, dispersive and long wavelength limit. Some…
We study ergodic properties of nonlinear Markov chains and stochastic McKean-Vlasov equations. For nonlinear Markov chains we obtain sufficient conditions for existence and uniqueness of an invariant measure and uniform ergodicity. We also…
We derive hydrodynamic equations from Vicsek-style dry active matter models in three dimensions (3D), building on our experience on the 2D case using the Boltzmann-Ginzburg-Landau approach. The hydrodynamic equations are obtained from a…
Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…
We introduce a positive definite single-particle distribution that is suitable for describing the transition from a macroscopic hydrodynamic to a microscopic kinetic description during the late stages of heavy-ion collisions in the presence…
Dissipative processes are pivotal for understanding the hydrodynamic evolution of hot and dense QCD matter created in relativistic nuclear collisions. The interplay of multiple conserved charges -- net baryon, strangeness, and electric…
We give a pedagogical review of relativistic hydrodynamics relevant to relativistic heavy ion collisions. Topics discussed include linear response theory derivation of 2nd order viscous hydrodynamics including the Kubo formulas, kinetic…
Exact solutions of the dispersive and modified equations are expressed in terms of special polynomials associated with rational solutions of the fourth Painleve equation, which arises as generalized scaling reductions of these equations.…
Nonlinear excitations of nuclear density are considered in the framework of semiclassical nonlinear nuclear hydrodynamics. Possible types of stationary nonlinear waves in nuclear media are analysed using Nonlinear Schroedinger equation of…
The construction of a generalized (higher-order) nonlinear thermo-hydrodynamics, based on a nonequilibrium ensemble formalism has been presented in the preceding article. The working of such theory is illustrated in the present one. We…
The new generalized kinetic equation is offered. This equation represents a hybrid Shakhov's equation and ellipsoidal statistical Holway's equation. Equation constants are expressed through such physically significant quantities, as…
A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of…
The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of…
General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves…