Compact travelling waves and peakon type solutions of several equations of mathematical physics and their Cellular Neural Network realization

Abstract

This paper deals with compact travelling waves and peakon type solutions of several equations of mathematical physics and their Cellular Neural Network (CNN) realization. More precisely, we study different generalizations of the Camassa–Holm equation, of the Korteweg–de Vries equation and the nonlinear PDE describing the vibrations of a chain of particles interconnected by springs. In many cases the waves develop cusp type singularities at the peaks. In the second part of the paper the CNN realization of the compact travelling waves is fulfilled and the corresponding geometrical illustrations of the interaction of these waves are given.