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The KP equation of plane elastodynamics

Berjamin, Harold
; 
Destrade, Michel
; 
Saccomandi, Giuseppe
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Identifiers
https://hdl.handle.net/10379/19087
 https://doi.org/10.13025/29881
Publication Date
2025-7-18
Keywords
KP equation, elastodynamics, Nonlinear elastodynamics, Incompressibility, Solitary waves, Burgers equation
Type
journal article
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Citation
Berjamin, Harold, Destrade, Michel, & Saccomandi, Giuseppe. (2025). The KP Equation of Plane Elastodynamics. SIAM Journal on Applied Mathematics, 85(4), 1458-1474. https://doi.org/10.1137/24M1710036
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.
Funder
European Union
Publisher
Society for Industrial and Applied Mathematics
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Rights
CC BY
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Mathematics (Scholarly Articles)