Nonlinear evolution equations for degenerate transverse waves in anisotropic elastic solids

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.Comment: 4 page

En flerfrekvenslösning till Burgers ekvation

A generalization of the single frequency Cole-Mendousse solution for the Burgers equation is shown. The solution is in the same form - a ratio between two Fourier series containing Bessel functions. The input is given as an arbitrary number of frequency components which can have any amplitude, frequency and phase. The solution is valid for any distance

Flerfrekvenslösning för periodiska och dämpade vågor

The solution for multi-frequency plane waves propagating through a dissipative and nonlinear medium is shown for some examples of periodic conditions. The expression may for any given condition be expressed analytically as a ratio of Fourier series with Bessel function coefficients. In the examples are shown how the final appearance of any initial wave always is a pure periodic wave in the lowest frequency existing in the problem - the period of the condition