Non-local symmetries, exact solutions and conservation laws for the coupled Lakshmanan–Porsezian–Daniel equations

The non-local symmetries of the coupled Lakshmanan–Porsezian–Daniel (LPD) equations are obtained with the help of the known Lax pair. By introducing an auxiliary variable, the coupled LPD equations are extended to a closed prolonged system and the non-local symmetries are localised to the Lie point symmetries of the prolonged system. Furthermore, based on the Lie point symmetries of the prolonged system, the exact solutions and non-local conservation laws of the coupled LPD equations are derived.