The nonlinear theory of two-dimensional ion-acoustic (IA) solitary waves and shocks (SWS) is revisited in a dissipative quantum plasma. The effects of dispersion, caused by the charge separation of electrons and ions and the quantum force associated with the Bohm potential for degenerate...

Brownian motors subject to a travelling wave potential are discussed. The Brownian motors move in the form of solitary waves. The solitary wave of the Brownian motor is evaluated analytically. Two expressions for the efficiency of Brownian motors are distinguished, one for generating force and...

In this paper, we investigate in detail the interactions of solitary waves in lattice systems with interaction potential V(q)=qn/n, where n is 4,6,8…, through their all possible collision types, and establish a quantitative connection between the scattering property of solitary waves and the...

The goal of this note is to construct a class of traveling solitary wave solutions for the compound Burgers–Korteweg–de Vries equation by means of a hyperbolic ansatz. A computational error in a previous work has been clarified.

In this paper, the compound Burgers–Korteweg–de Vries equation is studied by the first integral method, which is based on ring theory in commutative algebra. Several new kink-profile waves and periodic waves are established. The applications of these results to other nonlinear wave equations...

Considered the effect of traffic anticipation in the real world, a new anticipation driving car following model (AD-CF) was proposed by Zheng et al. Based on AD-CF model, adopted an asymptotic approximation between the headway and density, a new continuum model is presented in this paper. The...

The constraint equation which must hold for the reciprocal of a known solution for the Korteweg–de Vries (KdV) equation to be a solution itself is derived. These reciprocal solutions are required to satisfy a differential equation which is in fact a Painlevé equation. A differential...

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but is also closely connected with the microscopic car following model. The modified Korteweg-de Vries (mKdV) equation about the density wave in congested traffic has been derived near the...

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg–de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived...