Abstract
Investigated in this paper is the AB system, which is used to describe the baroclinic instability processes in the geophysical flows. By introducing an auxiliary function , we construct the quasi-periodic wave solutions of the AB system, and find that behaviors of the quasi-periodic waves are similar to those of the periodic waves of the AB system except for certain phase shift in each evolution period. Especially, when , the quasi-periodic waves develop into the periodic waves. Besides, it is found that under certain conditions the quasi-periodic waves degenerate into the irregular solitary waves, which are characterized by shape variations or appearances, splits, combinations and disappearances of certain bulges in the evolution.
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