对称不稳定大气中的孤立行波精确解

THE ACCURATE SOLITORY WAVE SOLUTIONS IN THE SYMMETRICAL UNSTABLE ATMOSPHERE

通过对二维准动量无辐散、无摩擦、密度非均匀分布的层结大气中基本气流切变对非线性方程组行波解的影响问题的研究，证明：（ａ）在对称稳定（ｑ＝Ｎ２Ｆ２－Ｓ４＞０）的大气中：非线性行波解为周期解，且其周期与相应的线性周期解的周期相等；（ｂ）在对称非稳定（ｑ＝Ｎ２Ｆ２－Ｓ４≤０）的大气中：存在两类非线性行波解，其性质是由参数Ｂ决定的。Ｂ＝（Ｎ２ｓｉｎ２φ－２Ｓ２ｓｉｎφｃｏｓφ＋Ｆ２ｃｏｓ２φ）／σ２。（１）当Ｂ＞０时为周期解，且其周期与相应的线性周期解的周期相等；（２）当Ｂ≤０时为孤立波解。

In this paper,through the study of the influences of the basic current tangential variations on the translatory wave solutions of non linear equations in the two dimensional non divegent quasi momentum,nonhomogeneous density and frictionless atmosphere,it is proved that (a)in the symmetrical stable atmosphere ( q=N 2F 2-S 4>0 ),the non linear translatory wave solution is periodic,and its period is equal to that of the corresponding linear periodic solution;and (b)in the symmetrical unstable atmosphere ( q=N 2F 2-S 4≤0 ),there are two kinds of non linear translatory ware solution and their properties are determined by the parameter B,B=(N 2 sin 2φ-2S 2 sin φ cos φ+F 2 cos 2φ)/σ 2 .Where (1) when B>0 ,the solution are periodic,and the period is equal to that of the corresponding linear periodic solution;and (2)when B≤0 ,the solutions are solitary wave.