Reductions of the (4 + 1)-dimensional Fokas equation and their solutions
| Autor: | Cao, Yulei, He, Jingsong, Cheng, Yi, Mihalache, Dumitru |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11071-020-05485-x |
| Popis: | An integrable extension of the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations is investigated in this paper.We will refer to this integrable extension as the (4+1)-dimensional Fokas equation. The determinant expressions of soliton, breather, rational, and semi-rational solutions of the (4 + 1)-dimensional Fokas equation are constructed based on the Hirota's bilinear method and the KP hierarchy reduction method. The complex dynamics of these new exact solutions are shown in both three-dimensional plots and two-dimensional contour plots. Interestingly, the patterns of obtained high-order lumps are similar to those of rogue waves in the (1 + 1)-dimensions by choosing different values of the free parameters of the model. Furthermore, three kinds of new semi-rational solutions are presented and the classification of lump fission and fusion processes is also discussed. Additionally, we give a new way to obtain rational and semi-rational solutions of (3 + 1)-dimensional KP equation by reducing the solutions of the (4 + 1)-dimensional Fokas equation. All these results show that the (4 + 1)-dimensional Fokas equation is a meaningful multidimensional extension of the KP and DS equations. The obtained results might be useful in diverse fields such as hydrodynamics, non-linear optics and photonics, ion-acoustic waves in plasmas, matter waves in Bose-Einstein condensates, and sound waves in ferromagnetic media. Comment: Nonlinear Dynamics, 99, (2020) 3013-3028 |
| Databáze: | arXiv |
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