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 study the problem of information propagation in brain microtubules. After considering the propagation of electromagnetic waves in a fluid of permanent electric dipoles, the problem reduces to the sine-Gordon wave equation in one space and one time dimensions. The problem of propagation of...

A justified modification of the real part of the complex non-linearity of a Schrödinger equation, recently proposed G. Kaniadakis, Phys. Rev. A 55 (1997) 941], allows us to obtain a new canonical quantum system obeying an exclusion–inclusion principle. The soliton solutions of this new...

Surface diffusion (SD) is a really ubiquitous phenomenon playing a highly important part in a wealth of natural and technological processes. The effect of SD is to move surface atoms, molecules and clusters and allow them to assemble into some desirable configurations or, vise versa, to destroy...

The nonlinear Klein–Gordon equation with a different potential that satisfies the degeneracy properties discussed in this paper possesses solitonic solutions that interact with long-range forces. We generalize the Ginzburg–Landau equation in such a way that the topological defects supported...

We consider elastic grains which repel upon contact according to the Hertz potential V=aδn,n2, where δ is the overlap between adjacent grains and report numerical and analytical studies for the case of a 1-D chain of spherical grains to show that an impulse initiated at an end of a chain of...