Infinitely many nonlocal symmetries and conservation laws for the (1+1)(1+1)-dimensional Sine–Gordon equation

Infinitely many nonlocal symmetries and infinitely many local and nonlocal conservation laws of the (1+1)(1+1)-dimensional Sine–Gordon (SG) equation are derived in terms of its Bäcklund transformation (BT). Some special nonlocal symmetries and nonlocal conservation laws are obtained from the linearized equations of the SG equation and its BT. Furthermore, one can derive infinitely many nonlocal symmetries from a known nonlocal symmetry, but also infinitely many nonlocal conservation laws from a known nonlocal conservation law. In addition, infinitely many local and nonlocal conservation laws can be directly generated from the BT through the parameter expansion procedure.