The KP equation of plane elastodynamics

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.

References in corpus (7)

• KP solitons in shallow water
• On the third- and fourth-order constants of incompressible isotropic elasticity
• Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
• Solitary and compact-like shear waves in the bulk of solids
• Nonlinear transverse waves in deformed dispersive solids
• Dispersive shock waves in the Kadomtsev-Petviashvili and Two Dimensional Benjamin-Ono equations
• Soliton Dynamics in a 2D Lattice Model with Nonlinear Interactions