Nonlinearly dispersive KP equations with new compacton solutions
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866918162025414656 |
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| author | Anco, Stephen C. Gandarias, Maria |
| author_facet | Anco, Stephen C. Gandarias, Maria |
| contents | A complete classification of compacton solutions is carried out for a generalization of the Kadomtsev-Petviashvili (KP) equation involving nonlinear dispersion in two and higher spatial dimensions. In particular, precise conditions are given on the nonlinearity powers in this equation under which a travelling wave can be cut off to obtain a compacton. Numerous explicit examples having various profiles are derived, including a quadratic function, powers of a cosine, and powers of Jacobi $\cn$ functions, all of which are symmetric. The cosine and $\cn$ symmetric compactons have an anti-symmetric counterpart. In comparison, explicit solitary waves of the generalized KP equation are found to have profiles given by a power of a sech and a reciprocal quadratic function. Kinematic properties of all of the different types of compactons and solitary waves are discussed, along with conservation laws of the generalized KP equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2103_15251 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Nonlinearly dispersive KP equations with new compacton solutions Anco, Stephen C. Gandarias, Maria Mathematical Physics Pattern Formation and Solitons A complete classification of compacton solutions is carried out for a generalization of the Kadomtsev-Petviashvili (KP) equation involving nonlinear dispersion in two and higher spatial dimensions. In particular, precise conditions are given on the nonlinearity powers in this equation under which a travelling wave can be cut off to obtain a compacton. Numerous explicit examples having various profiles are derived, including a quadratic function, powers of a cosine, and powers of Jacobi $\cn$ functions, all of which are symmetric. The cosine and $\cn$ symmetric compactons have an anti-symmetric counterpart. In comparison, explicit solitary waves of the generalized KP equation are found to have profiles given by a power of a sech and a reciprocal quadratic function. Kinematic properties of all of the different types of compactons and solitary waves are discussed, along with conservation laws of the generalized KP equation. |
| title | Nonlinearly dispersive KP equations with new compacton solutions |
| topic | Mathematical Physics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2103.15251 |