Concentrating on experimentally relevant cases we discuss nonlinear dynamics and deterministic chaos in F = 1 and F = 2 spinor Bose–Einstein condensates. A thorough numerical and analytical treatment of the equations of motion of symmetric F = 2 spin dynamics in the single-mode approximation elucidates the complex dynamics and uncovers regions of classical chaos in this important quantum gas sy...

We study the Whitham equations for the defocusing complex modified KdV (mKdV) equation. These Whitham equations are quasilinear hyperbolic equations and they describe the averaged dynamics of the rapid oscillations which appear in the solution of the mKdV equation when the dispersive parameter is small. The oscillations are referred to as dispersive shocks. The Whitham equations for the mKdV eq...

We make a detailed study on the dynamics of gain-assisted superluminal optical solitons in a three-state active-Raman-gain medium at room temperature. Using a method of multiple-scales we derive a high-order nonlinear Schrödinger equation with correction terms contributed from differential gain, nonlinear dispersion, delay in nonlinear refractive index, and third-order dispersion of the system....

We study a nonlinear pseudodifferential equation describing the dynamics of dislocations. The long time asymptotics of solutions is described by the self-similar profiles.

The noisy Burgers equation describing for example the growth of an interface subject to noise is one of the simplest model governing an intrinsically nonequilibrium problem. In one dimension this equation is analyzed by means of the MartinSiggia-Rose technique. In a canonical formulation the morphology and scaling behavior are accessed by a principle of least action in the weak noise limit. The...

We investigate the structure of the nonlocal closure relation in the kinetic equation for a soliton gas. This kinetic equation represents an integro-differential nonlinear system which has been recently shown to possess a number of remarkable properties and seems to be a representative of an entirely new class of integrable systems. In this paper, we identify the nonlocal kinetic closure relati...

In this paper we reconsider the classical nonlinear diffusivity equation of real gas in an heterogenous porous medium in light of the recent studies about the generalized fractional equation of conservation of mass. We first recall the physical meaning of the fractional conservation of mass recently studied by Wheatcraft and Meerschaert [22] and then consider the implications in the classical m...

Basic concepts of rarefied gas dynamics are given in a concise form. Some problems of rarefied gas flows are considered, namely, calculations of velocity slip and temperature jump coefficients, gas flow through a tube due to pressure and temperature gradients, and gas flow through a thin orifice. Results on the two last problems are given over the whole range of gas rarefaction. A methodology f...