Loop soliton interaction in an integrable nonlinear telegraphy model: reciprocal and Bäcklund transformations

Abstract

An integrable telegraphy equation linked, in turn, to the geometry of pseudospherical surfaces and a class of model nonlinear elastic stress–strain laws descriptive of ideally hard material response is investigated. A constant coefficient ideal formalism is introduced which leads to a reciprocal transformation between this nonlinear telegraphy equation and a system compatible with the classical sine-Gordon equation. A Bäcklund transformation is then constructed which is used to analyse two-loop soliton interaction. The latter exhibits a novel ‘exchange particle’ phenomenon.