Residual symmetry and Bäcklund transformations of model equations for shallow water waves

Abstract

ABSTRACT This paper is concerned with the application of the nonlocal residual symmetry analysis to model equations for shallow water waves. The localization procedure is applied such that the residual symmetries of the original system become local ones for a prolonged system. The Bäcklund transformations for the localized residual symmetries are obtained according to Lie's first theorem. Furthermore, the nth Bäcklund transformations are also obtained from the Lie point symmetry approach via the localization of the linear superposition of multiple residual symmetries.