This paper deals with the nonlinear problems of the two-layer shallow water wave modelin the atmosphere by the multiple scale method and points out that a nonlinear Benjamin-Ono equation may be obtained if the meridional disturbance wind is weak. Furthermore, thealgebraic solitary waves and nonlinear periodic waves are also calculated and the breakup ofan algebraic solitary wave at the initial time into two is discussed. It is found that the waveform steepens in this process, which is similar to the triggering process of squall lines inthe atmosphere. On the other hand, we also point out that when the meridional disturbancewind is strong, we may obtain a modified Benjamin-Ono equation, i. e. the Benjamin-Ono-KDV equation.
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