Geodesic
Longitudinal finite-amplitude wave in nonlinear homogeneous elastic medium. The equations of Landau-Murnaghan
Dalʹnevostočnyj matematičeskij žurnal, Tome 16 (2016) no. 2, pp. 160-168

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High-frequency asymptotic solution of the equations of motion for waves in nonlinear and homogeneous elastic mediumis is obtained, with predominantly longitudinal polarization. The main part of the solution is known from the consideration of the linear problem. The general solution except the main part contains two completely new part describing the excitation of the transverse wave and wave with the double frequency. These effects result in distortion of wave fronts, as well as to the weak attenuation of the primary longitudinal wave along the way. The inclusion of these nonlinear effects are important in the analysis of seismic waves. 
@article{DVMG_2016_16_2_a4,
     author = {M. A. Guzev and I. A. Molotkov},
     title = {Longitudinal finite-amplitude wave in  nonlinear homogeneous elastic medium. {The} equations of {Landau-Murnaghan}},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {160--168},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2016_16_2_a4/}
}
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M. A. Guzev; I. A. Molotkov. Longitudinal finite-amplitude wave in  nonlinear homogeneous elastic medium. The equations of Landau-Murnaghan. Dalʹnevostočnyj matematičeskij žurnal, Tome 16 (2016) no. 2, pp. 160-168. http://geodesic.mathdoc.fr/item/DVMG_2016_16_2_a4/