The existence of Riemann invariants in the one-dimensional equations of the non-linear theory of elasticity

The conditions for the existence of Riemann invariants of a one-dimensional system of equations of the non-linear theory of elasticity are investigate d. Haantjes' diagonalization criterion is used to determine the form of the elastic potential for which the system has six Riemann invariants or three Riemann invariants (for waves which propagate in one direction). In partic ular, it is shown that the Haantjes criterion is satisfied and there are th ree Riemann invariants in the case of the elastic potential for slightly-no n-linear weakly-anisotropic elastic media [1-3]. A procedure for computing Riemann invariants is described. The Riemann invariants are computed approx imately for a form of elastic potential which satisfies the Haantjes criter ion. (C) 1999 Elsevier Science Ltd. All rights reserved.