Lie symmetries, conservation laws and solitons for the AB system with time-dependent coefficients in nonlinear optics or fluid mechanics
- 13 Downloads
In this paper, the AB system with time-dependent coefficients for the ultrashort pulses in an inhomogeneous optical fibre or the marginally unstable baroclinic wave packets in an atmospheric or oceanic system is investigated via the Lie symmetry analysis. We obtain the Lie symmetries, reduced equations and group-invariant solutions. The nonlinear self-adjointness of the AB system is proved, and the conservation laws associated with the Lie symmetries are constructed. For the amplitude of the electric field in the inhomogeneous optical fibre or the amplitude of the wave packet in the atmospheric or oceanic system, and for the quantity associated with the occupation number which gives a measure of the atomic inversion in the inhomogeneous optical fibre or the quantity measuring the correction of the basic flow in the atmospheric or oceanic system, we get some solitons through the Lie symmetry transformations, whose amplitudes, widths, velocities and backgrounds are different from those of the given ones and can be adjusted via the Lie group parameters. We find a family of the ultrashort pulses propagating in the inhomogeneous optical fibre or a family of the marginally unstable baroclinic wave packets propagating in the atmospheric or oceanic system.
KeywordsNonlinear optics fluid mechanics AB system Lie symmetry analysis conservation laws soliton
PACS Nos05.45.Yv 47.35.Fg 02.30.Jr
This work has been supported by the National Natural Science Foundation for China under Grant Nos 11772017, 11805020, 11272023 and 11471050, by the Fund for State Key Laboratory for Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.
- 4.W X Ma, J. Fudan Univ. (Nat. Sci.) 33, 319 (1994)Google Scholar
- 20.C C Ding, Y T Gao, J J Su, G F Deng and S L Jia, Wave Random Complex, in press (2019), https://doi.org/10.1080/17455030.2018.1483092
- 29.W X Ma, Discret. Cont. Dyn. Sys. Ser. S 11, 707 (2018)Google Scholar
- 45.R K Dodd, J C Eilkck, J D Gibbon and H C Moms, Solitons and nonlinear wave equations (Academic Press, New York, 1982)Google Scholar