Geodesic
The ray type solution for the finite deformation waves in a physically linear nonlinear inhomogeneous medium
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 43, Tome 422 (2014), pp. 47-61 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is devoted to the ray types waves of finite deformation in the nonlinear, physically linear elastic media. The waves are a generalization of the Bland plane waves for the isotropic nonlinear media. For the waves the fast oscillation and slow oscillation parts are interacted during the process of propagation. Forms of the waves are adiabatically changed. An example of plane wave in the inhomogeneous media is considered. 
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     author = {A. P. Kachalov},
     title = {The ray type solution for the finite deformation waves in a~physically linear nonlinear inhomogeneous medium},
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A. P. Kachalov. The ray type solution for the finite deformation waves in a physically linear nonlinear inhomogeneous medium. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 43, Tome 422 (2014), pp. 47-61. http://geodesic.mathdoc.fr/item/ZNSL_2014_422_a3/

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[2] L. I. Lure, Nelineinaya teoriya uprugosti, Nauka, M., 1980 | MR

[3] A. P. Kachalov, “Prostranstvenno-vremennoi luchevoi metod dlya voln maloi deformatsii v nelineinoi uprugoi srede”, Zap. nauchn. semin. LOMI, 140, 1984, 61–72 | MR | Zbl

[4] D. R. Bland, Nonlinear dynamic elasticity, Blaisdel Publishing Company, Wolfham, 1969 | MR | Zbl