THE KP EQUATION OF PLANE ELASTODYNAMICS

Harold Berjamin; Michel Destrade; Giuseppe Saccomandi

doi:10.1137/24M1710036

THE KP EQUATION OF PLANE ELASTODYNAMICS

Harold Berjamin
, Michel Destrade
, Giuseppe Saccomandi

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1458-1474
Number of pages	17
Journal	SIAM Journal on Applied Mathematics
Volume	85
Issue number	4
DOIs	https://doi.org/10.1137/24M1710036
Publication status	Published - 2025
Externally published	Yes

Keywords

Burgers equation
incompressibility
KP equation
nonlinear elastodynamics
solitary waves

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10.1137/24M1710036

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title = "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.",

keywords = "Burgers equation, incompressibility, KP equation, nonlinear elastodynamics, solitary waves",

author = "Harold Berjamin and Michel Destrade and Giuseppe Saccomandi",

note = "Publisher Copyright: {\textcopyright} 2025 Society for Industrial and Applied Mathematics.",

year = "2025",

doi = "10.1137/24M1710036",

language = "English",

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T1 - THE KP EQUATION OF PLANE ELASTODYNAMICS

AU - Berjamin, Harold

AU - Destrade, Michel

AU - Saccomandi, Giuseppe

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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.

KW - Burgers equation

KW - incompressibility

KW - KP equation

KW - nonlinear elastodynamics

KW - solitary waves

UR - https://www.scopus.com/pages/publications/105011722547

U2 - 10.1137/24M1710036

DO - 10.1137/24M1710036

M3 - Article

AN - SCOPUS:105011722547

SN - 0036-1399

VL - 85

SP - 1458

EP - 1474

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 4

ER -

THE KP EQUATION OF PLANE ELASTODYNAMICS

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Keywords

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