Painlev$$\acute{\mathrm{e}}$$ integrable condition, auto-Bäcklund transformations, Lax pair, breather, lump-periodic-wave and kink-wave solutions of a (3+1)-dimensional Hirota–Satsuma–Ito-like system for the shallow water waves
| Autor: | Yu-Qi Chen, Cong-Cong Hu, Bo Tian, Yan Sun, Su-Su Chen, Qi-Xing Qu |
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| Rok vydání: | 2021 |
| Předmět: |
Physics
Integrable system Breather Applied Mathematics Mechanical Engineering One-dimensional space Aerospace Engineering Ocean Engineering Bilinear form Waves and shallow water Nonlinear Sciences::Exactly Solvable and Integrable Systems Control and Systems Engineering Lax pair Periodic wave Electrical and Electronic Engineering Nonlinear Sciences::Pattern Formation and Solitons Mathematical physics |
| Zdroj: | Nonlinear Dynamics. 106:765-773 |
| ISSN: | 1573-269X 0924-090X |
| DOI: | 10.1007/s11071-021-06686-8 |
| Popis: | In this paper, we investigate a (3+1)-dimensional Hirota–Satsuma–Ito-like system for the shallow water waves. We obtain a Painlev $$\acute{\mathrm{e}}$$ integrable condition of the system. By virtue of the truncated Painlev $$\acute{\mathrm{e}}$$ expansion, we get an auto-Backlund transformation under certain Painlev $$\acute{\mathrm{e}}$$ integrable condition. Based on the bilinear form, we give a bilinear auto-Backlund transformation and a Lax pair under certain Painlev $$\acute{\mathrm{e}}$$ integrable condition. We obtain that a breather and kink waves propagate under certain Painlev $$\acute{\mathrm{e}}$$ integrable condition. The breather has a peak and a trough and the height of the kink wave periodically increases or decreases during the propagation. Furthermore, we get the lump-periodic-wave and solitary-wave solutions and observe that the lump-periodic and solitary waves propagate under certain Painlev $$\acute{\mathrm{e}}$$ integrable conditions. During the propagation, the heights of the lump-periodic waves keep unchanged and height of the solitary wave periodically increases or decreases. |
| Databáze: | OpenAIRE |
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