Abstract
The interaction of shear horizontal (SH) waves in a two layered elastic medium and its mth harmonic component is studied. The dispersion relation is analysed to obtain the wave number-phase velocity pairs where the third and fifth harmonic resonance phenomena emerge. By employing an asymptotic perturbation method it is shown that the balance between the weak nonlinearity and dispersion yields a coupled nonlinear Schrodinger (CNLS) equation for the slowly varying amplitudes of the fundamental wave and its fifth harmonic component. The nonlinearity efects of the materials and the ratio of layers' thicknesses on the linear instabilities of solutions and the existence of solitary waves are examined.
| Original language | English |
|---|---|
| Pages (from-to) | 409-424 |
| Number of pages | 16 |
| Journal | Turkish World Mathematical Society Journal of Applied and Engineering Mathematics |
| Volume | 13 |
| Issue number | 2 |
| Publication status | Published - 2023 |
Bibliographical note
Publisher Copyright:© Isk University, Department of Mathematics, 2023; all rights reserved.
Keywords
- Nonlinear elasticity
- nonlinear waves
- perturbation methods
- solitary waves