Abstract
The paper presents theoretical results on the interaction of cubically nonlinear harmonic elastic plane waves in a nonlinear material described by the Murnaghan potential. The interaction of two harmonic transverse waves is studied using the method of slowly varying amplitude. Reduced and evolution equations and the Manley-Rowe relations are derived. An analysis is made of the mechanism of energy transfer from the strong pumping wave, which has frequency ω, to the weak signal wave, which has frequency 3ω because of this interaction. A switching mechanism for hypersonic waves in a nonlinear elastic material is described, which is similar to the switching mechanism observed in transistors
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