Some nonlinear dispersive waves arising in compressible hyperelastic plates

In this paper we study finite deformations in a pre-stressed, hyperelastic compressible plate. For small-amplitude nonlinear waves, we obtain equations that involve an amplitude parameter ε. 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.