Variable coefficient nonlinear systems derived from an atmospheric dynamical system
Tang Xiao-Yan(唐晓艳)a)†,Gao Yuan(高原)a), Huang Fei(黄菲)b), and Lou Sen-Yue(楼森岳) a)c)d)
a Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China; b Physical Oceanography Laboratory, Ocean University of China, Qingdao 266003, China; c Faculty of Science, Ningbo University, Ningbo 315211, China; d School of Mathematics, Fudan University, Shanghai 200433, China
Abstract Variable coefficient nonlinear systems, the Korteweg de Vries (KdV), the modified KdV (mKdV) and the nonlinear Schr?dinger (NLS) type equations, are derived from the nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane by means of the multi-scale expansion method in two different ways, with and without the so-called y-average trick. The non-auto-B?cklund transformations are found to transform the derived variable coefficient equations to the corresponding standard KdV, mKdV and NLS equations. Thus, many possible exact solutions can be obtained by taking advantage of the known solutions of these standard equations. Further, many approximate solutions of the original model are ready to be yielded which might be applied to explain some real atmospheric phenomena, such as atmospheric blocking episodes.
Received: 25 July 2008
Revised: 26 March 2009
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China (Grant Nos 10735030, 10547124,
90503006 and 40305009), the National Basic Research Program of China
(Grant Nos 2007CB814800 and 2005CB422301), Specialized Research Fund
for the Doctoral Program of Higher Education (Grant No 20070248120),
Program for Changjiang Scholars and Innovative Research Team in
University (Grant No IRT0734), the Scientific Research Starting
Foundation for Returned Overseas Chinese Scholars, Ministry of
Education, China and the Program for New Century Excellent Talents
in University of Ministry of Education of China (Grant No
NCET-05-0591).
Cite this article:
Tang Xiao-Yan(唐晓艳),Gao Yuan(高原), Huang Fei(黄菲), and Lou Sen-Yue(楼森岳) Variable coefficient nonlinear systems derived from an atmospheric dynamical system 2009 Chin. Phys. B 18 4622
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
