Residual Symmetry And Backlund Transformations Of Model Equations For Shallow Water Waves

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 Backlund transformations for the localized residual symmetries are obtained according to Lie's first theorem. Furthermore, the nth Backlund transformations are also obtained from the Lie point symmetry approach via the localization of the linear superposition of multiple residual symmetries.