Wave propagation in ideally hard inhomogeneous elastic materials associated with pseudospherical surfaces

Abstract

The nonlinear wave equation∂2T/∂X2=∂/∂t[∂T/∂t(1 +T2+X2)2] provides a Lagrangian description of one-dimensional stress propagation in a class of model inhomogeneous ideally hard elastic materials. The equation is privileged in that it is associated with pseudospherical surfaces with constant Gaussian curvature K script sign =-1. Here, exact representations for the stress distribution evolution in model elastic materials are obtained corresponding to classical Beltrami and Dini surfaces as well as a two-soliton pseudospherical surface generated via the classical Bäcklund transformation. © 2003 Elsevier Ltd. All rights reserved.