Soliton solutions, Darboux transformation of the variable coefficient nonlocal Fokas-Lenells equation

Under investigation in this paper is the variable coefficient nonlocal Fokas-Lenells equation. On the basis of the Lax pair, the infinitely-many conservation laws and Nth-fold Darboux transformation are constructed. Depending on zero seed solution, soliton solutions are derived via the Darboux transformation. Based on nonzero seed solution, breather solutions and rogue wave solutions are obtained. The behaviors of solutions are clearly analyzed graphically. The influences of variable coefficient for solutions are discussed. The different profiles of solitons, breathers and rogue waves are observed via selecting different variable coefficients. Furthermore, the interaction of solitons and the interaction of breathers for the variable coefficient nonlocal Fokas-Lenells equation are both elastic.