On nonlinear waves in an elastic solid

We describe the nonlinear dispersive dissipative evolution of strain waves in a solid in the limiting condition B similar to O(R/L), where B is the ch aracteristic amplitude of the wave, L its wavelength and R the radius of a solid rod. We also provide conditions on dissipation and dispersion for the propagation of either shocks or solitary waves of permanent form. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.