Nonlinear evolution equations for degenerate transverse waves in anisotropic elastic solids

TL;DR

This paper derives coupled evolution equations for transverse elastic waves in anisotropic solids, revealing nonlinear interactions absent in isotropic media, with specific examples for cubic crystals.

Contribution

It introduces new coupled evolution equations for transverse waves in anisotropic elastic solids, highlighting nonlinear interactions along specific symmetry axes.

Findings

Quadratic nonlinear coupling exists in anisotropic but not isotropic media.

Derived coupled evolution equations for two-fold and three-fold symmetry axes.

Illustrated results with examples from cubic crystal structures.

Abstract

Transverse elastic waves behave differently in nonlinear isotropic and anisotropic media. Quadratically nonlinear coupling in the evolution equations for wave amplitudes is not possible in isotropic solids, but such a coupling may occur for certain directions in anisotropic materials. We identify the expression responsible for the coupling and we derive coupled canonical evolution equations for transverse wave amplitudes in the case of two-fold and three-fold symmetry acoustic axes. We illustrate our considerations by examples for a cubic crystal.