Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation**Project supported by the National Natural Science Foundation of China (Grant Nos. 11347183, 11275129, 11305106, 11365017, and 11405110) and the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y7080455 and LQ13A050001).

Abstract

In nonlinear physics, it is very difficult to study interactions among different types of nonlinear waves. In this paper, the nonlocal symmetry related to the truncated Painlevé expansion of the (2+1)-dimensional Burgers equation is localized after introducing multiple new variables to extend the original equation into a new system. Then the corresponding group invariant solutions are found, from which interaction solutions among different types of nonlinear waves can be found. Furthermore, the Burgers equation is also studied by using the generalized tanh expansion method and a new Bäcklund transformation (BT) is obtained. From this BT, novel interactive solutions among different nonlinear excitations are found.