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本文利用多重尺度方法研究了大气中两层浅水波方程的非线性问题。文中指出:在经向扰动速度不太强的情况下,可以得到一个非线性Benjamin-Ono方程,并对它的代数孤立波和周期波进行了计算。同时还讨论了代数孤立波的演变过程,发现它在演变过程中可发生分裂,并产生波形的突陡,这可解释大气中的飑线过程。另外还指出:在经向扰动速度较强的情况下,可以得到一个修正的Benjamin-Ono方程,即Benjamin-Ono-KDV方程。
In this paper, the multi-scale method is used to study the nonlinear problem of two shallow wave equations in the atmosphere. It is pointed out in this paper that a non-linear Benjamin-Ono equation can be obtained under the condition that the velocity of meridional perturbation is not too strong, and its algebraic solitary waves and periodic waves are calculated. The evolution of algebraic solitary wave is also discussed. It is found that it can split during the evolution and produce steep waveforms, which can explain the 飑 line process in the atmosphere. In addition, it is pointed out that a modified Benjamin-Ono equation, the Benjamin-Ono-KDV equation, can be obtained in the case of a strong perturbation of the meridional direction.