We review spectral theory of soliton gases in integrable dispersive hydrodynamic systems. first present a phenomenological approach based on the consideration phase shifts pairwise collisions and leading to kinetic equation for non-equilibrium gas. Then more detailed is presented which gas dynamics are modelled by thermodynamic type limit modulated finite-gap solutions Korteweg-de Vries focusin...

Gas bearings have been widely applied to high-speed rotating machines due their low friction and high rotational speed advantages. Nevertheless, gas lubrication is viscosity compressible. It causes the bearing-rotor system easy produce self-excited vibration, which leads instability of rotor hinders increase speed. necessary study nonlinear behaviors aerostatic vibration system, especially cons...

Some recent experimental observations have been shown that inclusion of electron collisions damping in inertial Alfvén wave (IAW) dynamics may be important for laboratory as well as space plasmas. This paper presents the numerical simulation of model equation governing the nonlinear dynamics of IAW in low-beta plasmas. When the nonlinearity arises due to the ponderomotive force and Joule heatin...

Abstract The dynamics of sound in a fluid is intrinsically nonlinear. We derive the consequences this fact for analogue gravitational field experienced by waves, first describing generally how nonlinearity equation phase fluctuations back-reacts on definition background providing effective space-time metric. Subsequently, we use analytical tool Riemann invariants one-dimensional motion to sourc...

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical m...

Relativistic effects in the thermodynamical properties of interacting particle systems are investigated within the framework of the relativistic direct interaction theory in various forms of dynamics. In the front form of relativistic dynamics an exactly solvable model of a one-dimensional hard spheres gas is formulated and an equation of state and thermodynamical potentials for such a gas are ...

Group analysis developed especially for differential equations allows systematic study of solutions of the full Boltzmann kinetic equation. The study is connected with the admitted Lie group of infinitesimal transformations. Group classification of admitted group gives all representations of essentially different invariant solutions. Ususally the group classification is quite difficult to do: i...

1 Abstract Self-consistent mouvement of initial perturbation in density, velocity and grav-itation potentail on the background of the stationary cylindrical configuration of the gas with gravitation and pressure in Lagrange variables have been studied. The nonlinear partial differential equation for description radius motion has been obtained. The linearization of this equation is reduced to a ...

Nonlinear dynamics of wave packets in two-dimensional parity-time-symmetric optical lattices near the phase transition point are analytically studied. A fourth-order equation is derived for the envelope of these wave packets. A pyramid diffraction pattern is demonstrated in both the linear and nonlinear regimes. Blow-up is also possible in the nonlinear regime for both focusing and defocusing n...