The KP equation of plane elastodynamics
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918096724295680 |
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| author | Berjamin, Harold Destrade, Michel Saccomandi, Giuseppe |
| author_facet | Berjamin, Harold Destrade, Michel Saccomandi, Giuseppe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17411 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The KP equation of plane elastodynamics Berjamin, Harold Destrade, Michel Saccomandi, Giuseppe Mathematical Physics Pattern Formation and Solitons 74J30 (Primary) 74J35 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. |
| title | The KP equation of plane elastodynamics |
| topic | Mathematical Physics Pattern Formation and Solitons 74J30 (Primary) 74J35 |
| url | https://arxiv.org/abs/2504.17411 |