Mielke, Alexander Uniqueness of the surface-wave speed: A proof that it is independent of the Stroh formalism. (English) Zbl 1043.74025 Math. Mech. Solids 9, No. 1, 5-15 (2004). 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. Cited in 18 Documents MSC: 74J15 Surface waves in solid mechanics 74H25 Uniqueness of solutions of dynamical problems in solid mechanics Keywords:surface impedance matrix; Riccati equation Citations:Zbl 1018.74020 PDFBibTeX XMLCite \textit{A. Mielke}, Math. Mech. Solids 9, No. 1, 5--15 (2004; Zbl 1043.74025) Full Text: DOI