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

The nonlinear wave equation (delta2T)/(deltaX2) = (delta)/(deltat)[(deltaT)/(deltat)/(1 + T-2 + X-2)(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 = -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 Backlund transformation. (C) 2003 Elsevier Ltd. All rights reserved.