Abstract
Consideration is given to the nonlinear theory of elastic waves with cubic nonlinearity. This nonlinearity is separated out, and the interaction of four harmonic waves is studied. The method of slowly varying amplitudes is used. The shortened and evolution equations, the first integrals of these equations (Manley–Rowe relations), and energy balance law for a set of four interacting waves (quadruplet) are derived. The interaction of waves is described using the wavefront reversal scheme
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Rushchitsky, J.J., Cattani, C. Evolution Equations for Plane Cubically Nonlinear Elastic Waves. International Applied Mechanics 40, 70–76 (2004). https://doi.org/10.1023/B:INAM.0000023812.41455.63
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DOI: https://doi.org/10.1023/B:INAM.0000023812.41455.63