Compact travelling waves and peakon type solutions of several equations of mathematical physics and their cellular neural network realization

The paper deals with compact travellig waves and peakons type solutions of several equations of mathematical physiscs and their CNN realization. More precisely we study different generalizations of the Camassa-Holm equation, of the Korteweg-deVries 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 and 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 interactions of these waves are given.