中国物理B ›› 2009, Vol. 18 ›› Issue (11): 4622-4635.doi: 10.1088/1674-1056/18/11/004

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Variable coefficient nonlinear systems derived from an atmospheric dynamical system

唐晓艳1, 高原1, 楼森岳2, 黄菲3   

  1. (1)Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China; (2)Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China;Faculty of Science, Ningbo University, Ningbo 315211, China \addressd)School of Mathematics, Fudan University, Shanghai 200433, China; (3)Physical Oceanography Laboratory, Ocean University of China, Qingdao 266003, China
  • 收稿日期:2008-07-25 修回日期:2009-03-26 出版日期:2009-11-20 发布日期:2009-11-20
  • 基金资助:
    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).

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)   

  1. 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
  • Received:2008-07-25 Revised:2009-03-26 Online:2009-11-20 Published:2009-11-20
  • Supported by:
    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).

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摘要： 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\"acklund 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.

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.

Key words: nonlinear inviscid barotropic nondivergent vorticity equation, variable coefficient equations, non-auto-B?cklund transformation

中图分类号:  (Solitons)

  • 05.45.Yv
92.60.-e (Properties and dynamics of the atmosphere; meteorology) 02.30.Jr (Partial differential equations)