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Uniqueness of the surface-wave speed: A proof that it is independent of the Stroh formalism. (English) Zbl 1043.74025

Summary: It is well-known in surface-wave theory that the secular equation for the surface-wave speed \(v\) can be written as \(\det M=0\) in terms of the surface impedance matrix \(M\). It has recently been shown by the present author [Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No. 2026, 2223–2543 (2002; Zbl 1018.74020)] that \(M\) satisfies a simple algebraic Riccati equation. It is shown in the present paper that a purely matrix algebraic analysis of this equation suffices to prove that whenever a surface wave exists it is unique.

MSC:

74J15 Surface waves in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics

Citations:

Zbl 1018.74020
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