Modulated waves and helicoidal pseudospherical surfaces in nonlinear inhomogeneous elasticity

The nonlinear wave equation ∂2T/∂X2=∂/∂t [∂T/∂t / (1+x2+T2)2] provides a Lagrangian description of one-dimensional stress propagation in a class of model inhomogeneous ideally hard elastic materials. It is associated with the geometry of pseudospherical surfaces and, as such, is integrable and admits an auto-Baecklund transformation. Here, modulated waves associated with helicoidal pseudospherical surfaces are investigated.