The wave motion characteristic of large-scale barotropic atmospheric circulation, which can be described by the original nonlinear shallow water equations, is important for comprehending the climatic change. Employing the complex solution of linear equation, and transplanting it twice, the new analytic solution of disturbed height field of the nonlinear evolution equation is obtained which is constructed by the basic flow term and fluctuation term. The basic flow is codetermined by the wave number, wave velocity, β effect, radius of deformation and arbitrary function of time. The fluctuation term is related to β effect, and displays that in the disturbed height field there exist the periodic wave and solitary wave of curved face, which modulate each other and present instability; several periodic-solitary waves can propagate independently when they appear simultaneously; the arbitrary function of time in the fluctuation term has a modulation effect on the amplitude of periodic-solitary wave, and can control the occurrence, development and vanishing of wave. The results have a certain theoretical reference value for studying the atmospheric fluctuation phenomena and climatic change.