The KP equation of plane elastodynamics
H. Berjamin, M. Destrade, G. Saccomandi (2025). "The KP equation of plane elastodynamics", SIAM Journal on Applied Mathematics 85(4), 1458-1474. https://doi.org/10.1137/24M1710036
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.
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Nonlinear elastodynamics, KP equation, Incompressibility, Solitary waves, Burgers equation