New Bäcklund transformations of the (2 + 1)-dimensional Burgers system related to residual symmetry

Abstract

Through truncated Painleve expansion of the (2 + 1)-dimensional Burgers system the residual symmetry is obtained and localized to a local one in an enlarged system by introducing new dependent variables. Using Lie’s first theorem, the Backlund transformation related to the localized residual symmetry is derived. Furthermore, the N-th-Backlund transformation of the (2 + 1)-dimensional Burgers system, which is expressed by determinants in a compact form, related to the symmetry of linear superposition of multiple residual symmetries is obtained through localization procedure.