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本文讨论大气中非线性波动的非频散解。在引入相角函数后,把大气中非线性偏微分方程组化为非线性常微分方程组。在系统的平衡点及奇异点附近讨论轨线性质,得到了非线性波动的一系列解析表达式。本文第一部分主要讨论二个问题1.拟能及拟能影响函数与非线性波解的关系,通过对拟能影响函数的讨论,可以判定周期解、孤波解、间断周期解与间断孤波解的存在条件,并且指出外界扰动若使拟能影响函数发生微小变化,则会导致孤立波的产生。2.间断周期解存在性讨论及函数逼近方法的使用。在求近似解过程中往往采用Taylor展开方法,但带来许多麻烦,本文对拟能影响曲线采用函数逼近的方法收到了良好的效果。
This article discusses the non-dispersive solutions to nonlinear fluctuations in the atmosphere. After the introduction of the phase angle function, the nonlinear partial differential equations in the atmosphere are transformed into nonlinear ordinary differential equations. The properties of trajectories are discussed in the vicinity of the system equilibrium point and the singular point. A series of analytic expressions of nonlinear fluctuations are obtained. The first part of this paper mainly discusses two questions: 1. To be able and to be able to affect the relationship between function and nonlinear wave solutions. By discussing the quasi-influence function, we can determine the periodic solutions, solitary wave solutions, discontinuous periodic solutions and discontinuous solitary waves The existence conditions of the solution are also pointed out. If the perturbation of the outside world is made to make small changes in the function to be influenced, the solitary wave will be generated. Existence of discontinuous periodic solutions and the use of function approximation methods. In the process of seeking approximate solutions, the Taylor expansion method is often used, but it brings a lot of troubles. This paper has received good results on the function approximation method which can influence the curve.