Source: Osaka J. Math.
Volume 49, Number 2
In this paper we study geometric properties of the slowness
surface of the system of crystal acoustics for cubic crystals
in the special case when the stiffness constants satisfy the
condition $a = -2b$. The paper is a natural continuation
of the paper  in which related properties were studied
for general constants $a$ and $b$, but assuming that we were
in the nearly isotropic case, in which case $a - b$ has to
be small. We also take this opportunity to correct a statement
made in : see Remark 1.3.
A. Bannini and O. Liess: Estimates for Fourier transforms of surface carried densities on surfaces with singular points, II, Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 52 (2006), 211–232.
R. Courant and D. Hilbert: Methods of mathematical physics, II, Partial differential equations, Wiley Classics Library, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1989.
G.F.D. Duff: The Cauchy problem for elastic waves in an anisotropic medium, Phil. Transactions Royal Soc. London, Ser. A 252 (1960), 249–273.
Mathematical Reviews (MathSciNet): MR111293
B. Gross and J. Harris: Real algebraic curves, Ann. E.N.S., 4\textsuperscripte série t.14, (1981), 157–182.
Mathematical Reviews (MathSciNet): MR631748
L.D. Landau and E.M. Lifshits: Theoretical Physics; Elasticity Theory, first Russian edition, Mir, Moscow, 1953. (Available also in many other editions and translations in many languages.)
O. Liess: Conical Refraction and Higher Microlocalization, Springer Lecture Notes in Mathematics 1555, 1993.
O. Liess: Estimates for Fourier transforms of surface-carried densities on surfaces with singular points, Asymptotic analysis 37 (2004), 329–363.
O. Liess: Decay estimates for the solutions of the system of crystal acoustics for cubic crystals, Kokyoroku series of the RIMS in Kyoto 1412 (2005), 1–13.
O. Liess: Curvature properties of the slowness surface of the system of crystal acoustics for cubic crystals, Osaka J. Math. 45 (2008), 173–210.
O. Liess: Decay estimates for the solutions of the system of crystal acoustics for cubic crystals, Asymptotic analysis 64 (2009), 1–27.
G.F. Miller and M.J.P. Musgrave: On the propagation of elastic waves in aleotropic media, III, Media of cubic symmetry, Proc. Royal Soc. London 236 (1956), 352–383.
Mathematical Reviews (MathSciNet): MR79433
M.J.P. Musgrave: Crystal Acoustics, Holden and Day, San Francisco, 1979.
N. Ortner and P. Wagner: Fundamental matrices of homogeneous hyperbolic systems. Applications to crystal optics, elastodynamics, and piezoelectromagnetism, ZAMM 84 (2004), 314–346.
H.G. Zeuthen: Sur les courbes du quatrième ordre, Mathematische Annalen 7, (1874), 410–432.