Lie Symmetries and Conservation Laws of Fokas-Lenells Equation and Two Coupled Fokas-Lenells Equations by the Symmetry/Adjoint Symmetry Pair Method

The Fokas-Lenells equation and its multi-component coupled forms have attracted the attention of many mathematical physicists. The Fokas-Lenells equation and two coupled Fokas-Lenells equations are investigated from the perspective of Lie symmetries and conservation laws. The three systems have been turned into real multi-component coupled systems by appropriate transformations. By procedures of symmetry analysis, Lie symmetries of the three real systems are obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair method, which depends on Lie symmetries and adjoint symmetries. The relationships between the multiplier and the adjoint symmetry are investigated.