DARBOUX TRANSFORMATION, EXACT SOLUTIONS OF THE VARIABLE COEFFICIENT NONLOCAL FOKAS-LENELLS EQUATION

In this paper, a (1+1)-dimensional integrable variable coefficient nonlocal Fokas-Lenells (NFL) equation is studied. On the basis of the Lax pair, the Darboux transformation of the variable coefficient NFL equation is constructed at the first time and an explicit form of the N-fold Darboux transformation is given. The exact solutions of the variable coefficient NFL equation are derived using the zero seed solution and the nonzero seed solution according to the Darboux transformation. Subsequently, one-soliton solution, two-soliton solution, and kink solution with periodic waves are obtained by choosing the proper parameters and plotting the corresponding figures. With the help of figures, the behaviors of the obtained solutions are revealed and it is possible to find that the interaction between solitons is elastic no matter the coefficient function is constant or arbitrary variable. In addition, this paper also indicates that the exact solutions of the variable coefficient NFL equation are more general than its constant coefficient form.