Some nonlinear dispersive waves arising in compressible hyperelastic plates. (English) Zbl 1213.74182
Summary: We study finite deformations in a pre-stressed, hyperelastic compressible plate. For small-amplitude nonlinear waves, we obtain equations that involve an amplitude parameter \(\epsilon \). Using an asymptotic perturbation technique, we derive a new family of two-dimensional nonlinear dispersive equations. This family includes the KdV, Kadomtsev-Petviashvili and Camassa-Holm equations.
MSC:
| 74J30 | Nonlinear waves in solid mechanics |
| 34E05 | Asymptotic expansions of solutions to ordinary differential equations |
| 74B20 | Nonlinear elasticity |
| 74K20 | Plates |
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