The KP equation of plane elastodynamics
Mathematical Physics
2025-07-21 v1 math.MP
Pattern Formation and Solitons
Abstract
The propagation of nonlinear and dispersive waves in various materials can be described by the well-known Kadomtsev-Petviashvili (KP) equation, which is a (2+1)-dimensional partial differential equation. In this paper, we show that the KP equation can be used to describe the in-plane motion of compressible elastic solids with dispersion. Furthermore, a modified KP equation with cubic nonlinearity is obtained in the case of incompressible solids with dispersion. Then, several solutions of these partial differential equations are discussed and computed using a Fourier spectral method. In particular, both equations admit solitary wave solutions.
Cite
@article{arxiv.2504.17411,
title = {The KP equation of plane elastodynamics},
author = {Harold Berjamin and Michel Destrade and Giuseppe Saccomandi},
journal= {arXiv preprint arXiv:2504.17411},
year = {2025}
}