A recursive generation of local higher-order sine–Gordon equations and their Bäcklund transformation

A new hierarchy of local nonlinear evolution equations is generated by a recursion operator and its explicit inverse. It is shown that this hierarchy satisfies a canonical geometrical scheme and that it contains as special cases the sine–Gordon and Liouville equations in laboratory coordinates. A generalization of the well-known Bäcklund transformation and nonlinear superposition formula for the sine–Gordon equation is also obtained.