Nonlocal symmetry and exact solutions of the (2+1)- dimensional breaking soliton equation

Abstract

The nonlocal symmetry which is obtained from Lax pair and the residual symmetry relating to truncated Painlevé expansion are derived. The link between the residual symmetry and the nonlocal symmetry which is obtained from Lax pair is presented. The residual symmetry can be localized to Lie point symmetry by prolonging the original equation to a larger system. The finite transformation of the residual symmetry is equivalent to the second type of Darboux transformation. Furthermore, applying the standard Lie group approach to the prolonged system, new similarity reductions and the exact interaction solutions between solitons and cnoidal periodic waves are given, which is difficult to be found by other traditional methods.