Using a long wave expansion we study the asymptotic solutions near a critical point of a multi-anticipative car-following model. A suitable rescaling of the variables then yields a modified Korteweg–de Vries (MKdV) equation with higher order corrections. An equation of this general form has...

We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison is made between exact solutions and solutions of the...

We present one-dimensional (1D) stability analysis of a recently proposed method to filter and control localized states of the Bose–Einstein condensate (BEC), based on novel trapping techniques that allow one to conceive methods to select a particular BEC shape by controlling and manipulating...

The decay rate for a particle in a metastable cubic potential is investigated in the quantum regime by the Euclidean path integral method in semiclassical approximation. The imaginary time formalism allows one to monitor the system as a function of temperature. The family of classical paths,...

Two-dimensional stability of a controlled Bose-Einstein condensation state, in the form of a nonlinear Schrödinger soliton [JETP Lett. <Emphasis Type="Bold">80 535 (2004)], is studied for the condensations with both repulsive and attractive inter-atom interactions. The Gross-Pitaevski equation is solved numerically,...</emphasis>