Infinitely many generalized symmetries and Painlevé analysis of a (2 + 1)-dimensional Burgers system

Infinitely many generalized symmetries of a coupled (2 + 1)-dimensional Burgers system are obtained by means of the formal series symmetry approach. It is found that the generalized symmetries constitute a closed infinite-dimensional Lie algebra. Three interesting special cases are presented, including a closed infinite-dimensional Lie algebra and a Kac–Moody–Virasoro-type Lie symmetry algebra. From the first one of the positive flow, a new integrable coupled system of the modified Korteweg–de Vries equation and the potential Boiti–Leon–Manna–Pempinelli equation is constructed. In addition, it is demonstrated that the coupled Burgers system can pass the Painlevé test. (paper)