Variable coefficient nonlinear systems derived from an atmospheric dynamical system  

作　　者：唐晓艳 高原 黄菲 楼森岳 

机构地区：[1]Department of Physics,Shanghai Jiao Tong University [2]Physical Oceanography Laboratory,Ocean University of China [3]Faculty of Science,Ningbo University [4]School of Mathematics,Fudan University

出　　处：《Chinese Physics B》2009年第11期4622-4635,共14页中国物理B（英文版）

基　　金：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;the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No NCET-05-0591)

摘　　要：Variable coefficient nonlinear systems, the Korteweg de Vries （KdV）, the modified KdV （mKdV） and the nonlinear Schrǒdinger （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-Bǎcklund 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.Variable coefficient nonlinear systems, the Korteweg de Vries （KdV）, the modified KdV （mKdV） and the nonlinear Schrǒdinger （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-Bǎcklund 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.

关 键 词：nonlinear inviscid barotropic nondivergent vorticity equation variable coefficient equations non-auto-Bǎcklund transformation 

分 类 号：N93[自然科学总论]