Solitary Wave Solutions of a Hyperelastic Dispersive Equation

Abstract

This paper explores solitary wave solutions arising in the deformations of a hyperelastic compressible plate. Explicit traveling wave solution expressions with various parameters for the hyperelastic compressible plate are obtained and visualized. To analyze the perturbed equation, we employ geometric singular perturbation theory, Melnikov methods, and invariant manifold theory. The solitary wave solutions of the hyperelastic compressible plate do not persist under small perturbations for wave speed c>−βk2. Further exploration of nonlinear models that accurately depict the persistence of solitary wave solution on the significant physical processes under the K-S perturbation is recommended.

Keywords

• hyperelastic compressible plate
• solitary wave solutions
• geometric singular perturbation theory
• Hamiltonian function
• bifurcation theory
• Melnikov methods