地-气耦合气候动力系统的解析研究

ENSO事件是影响全球气候表象大尺度的海洋-大气耦合系统,其规律和预防的研究,为当前国际学术界关注的对象。非线性摄动理论和方法在国际学术界研究中是十分热门的。许多学者做了一类常微分方程非线性奇摄动边值问题, 反应扩散问题, 椭圆型边值问题,双曲型初始边值问题,非线性方程奇摄动问题的冲击层解等。文章讨论一类大气物理中海-气现象的ENSO模型,在一定条件下,利用摄动理论和方法较简捷得到相应非线性问题解组的任意次近似的渐近展开式。

Analytic Study on Land-air Coupled Climate Dynamical System

The ENSO(El Nio/La Nio Southern Oscillation) is an exceptional event in the tropical atmosphere and ocean.It describes phenomenon of circular climate.ESNO event is a larger scale ocean-atmosphere coupled system,which affects global climate.It is a complicated nonlinear system.Its appearance affects badly climate for the global each area and the environment and so on.The global economic development and human living are gotten grievous influence and it brings many calamities.Thus to study its rule and prevention there is recently very attractive object of study in the international academic circles.Many scholars made more studies for its local and whole behaviors using different methods,such as self-anamnestic principle,by the method of Fokker-Plank equation,and the higher order singular pedigree and predictable study,rapid change on boundary,indeterminate adapive cortrol,multi-cogradient method,perturbed situation and so on.Nonlinear perturbed theory is a very attractive object of study in the international academic circles.Many scholars considered a class of singularly perturbed nonlinear boundary value problems for the ordinary differential equation,the reaction diffusion equations,the boundary value problems of elliptic equation,the initial boundary value problems of hyperbolic eqaution,the shock layer solution of nonlinear equation for singularly perturbed problem and so on.In this paper,the sea-air phenomena ENSO in a class of atmospheric physics is discussed.Under suitable conditions,using a perturbed theory and method,we obtain simple and rapid arbitrary order to approximate asymptotic expansion of solution for the corresponding nonlinear problem.