Various approximate solutions in wave equation for cord under non-gravitational field

Abstract

A wave equation for a cord (thin rope) that describes waves propagating on a cord under the non-gravitational field was derived in a previous paper when a tension T of a cord is constant. And, it was found that this wave equation has a unimodal solitary wave solution or a periodic sine wave solution when its amplitude is sufficiently small. The present paper is a sequel to the previous paper and here n -th power of the former wave solution or (2 n − 1)-th power of the latter wave solution is found to be also an approximate solution of the wave equation for the cord. This time it is made clear that the wave equation has a kink or anti-kink wave solution. Moreover, stabilities of these approximate wave solutions are investigated. As a last argument, collisions between kink · kink or kink · anti-kink waves are studied and their appearances are plotted.