Chin. Phys. B, 2016, Vol. 25(4): 040202    DOI: 10.1088/1674-1056/25/4/040202
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# (2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect

Jin-Yuan Li(李近元)1,2,3, Nian-Qiao Fang(方念乔)1, Ji Zhang(张吉)2,3, Yu-Long Xue(薛玉龙)4, Xue-Mu Wang(王雪木)4, Xiao-Bo Yuan(袁晓博)1
1 School of Ocean Sciences, China University of Geosciences (Beijing), Beijing 100083, China;
2 Marine Geology and Hydrology Research Laboratory, Guodian New Energy Technology Research Institute, Beijing 102209, China;
3 Zhong Neng Power-Tech Development Company Limited, Beijing 100034, China;
4 Marine Geological Institute of Hainan Province, Haikou 570206, China
Abstract  In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.
Keywords:  (2+1)-dimensional dissipation nonlinear Schrödinger equation      envelope Rossby solitary waves      chirp effect      two-soliton solutions
Received:  06 September 2015      Revised:  25 November 2015      Published:  05 April 2016
 PACS: 02.30.Jr (Partial differential equations) 47.35.Fg (Solitary waves) 92.10.Hm (Ocean waves and oscillations)
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 41406018).
Corresponding Authors:  Jin-Yuan Li     E-mail:  lijinyuan198007@sina.com