Bilinear Backlund transformation, Lax pair and interactions of nonlinear waves for a generalized (2+1)-dimensional nonlinear wave equation in nonlinear optics/fluid mechanics/plasma physics

被引：43
作者：
Zhao, Xin [1 ,2 ]
Tian, Bo [1 ,2 ]
Tian, He-Yuan [1 ,2 ]
Yang, Dan-Yu [1 ,2 ]
机构：
[1] Beijing Univ Posts & Telecommun, State Key Lab Informat Photon & Opt Commun, Beijing 100876, Peoples R China
[2] Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China
来源：
NONLINEAR DYNAMICS | 2021年 / 103卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Nonlinear optics; Fluid mechanics; Plasma physics; (2+1)-dimensional nonlinear wave equation; Bilinear Bä cklund transformation; Lax pair; Interactions of nonlinear waves; Noise perturbations;
D O I：
10.1007/s11071-020-06154-9
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
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.
引用
收藏
页码：1785 / 1794
页数：10
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