Bilinear Bäcklund transformation, Lax pair and interactions of nonlinear waves for a generalized (2 + 1)-dimensional nonlinear wave equation in nonlinear optics/fluid mechanics/plasma physics
| Autor: | Dan-Yu Yang, He-Yuan Tian, Bo Tian, Xin Zhao |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Applied Mathematics Mechanical Engineering One-dimensional space Aerospace Engineering Nonlinear optics Ocean Engineering Fluid mechanics Invariant (physics) 01 natural sciences Nonlinear system Nonlinear Sciences::Exactly Solvable and Integrable Systems Classical mechanics Amplitude Control and Systems Engineering 0103 physical sciences Lax pair Electrical and Electronic Engineering Rogue wave Nonlinear Sciences::Pattern Formation and Solitons 010301 acoustics |
| Zdroj: | Nonlinear Dynamics. 103:1785-1794 |
| ISSN: | 1573-269X 0924-090X |
| DOI: | 10.1007/s11071-020-06154-9 |
| Popis: | In this paper, outcomes of the study on the Backlund transformation, Lax pair, and interactions of nonlinear waves for a generalized (2 + 1)-dimensional nonlinear wave equation in nonlinear optics, fluid mechanics, and plasma physics are presented. Via the Hirota bilinear method, a bilinear Backlund transformation is obtained, based on which a Lax pair is constructed. Via the symbolic computation, mixed rogue–solitary and rogue–periodic wave solutions are derived. Interactions between the rogue waves and solitary waves, and interactions between the rogue waves and periodic waves, are studied. It is found that (1) the one rogue wave appears between the two solitary waves and then merges with the two solitary waves; (2) the interaction between the one rogue wave and one periodic wave is periodic; and (3) the periodic lump waves with the amplitudes invariant are depicted. Furthermore, effects of the noise perturbations on the obtained solutions will be investigated. |
| Databáze: | OpenAIRE |
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