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In this paper, we propose the bilinearization of the Fokas-Lenells equation(FLE) with a vanishing boundary condition. In the proposed bilinearization wemake use of an auxiliary function to convert the trilinear equations into a setof bilinear equations. We obtain bright 1-soliton, 2- soliton solutions andpresent the scheme for obtaining N soliton solution. In the soliton solutionthe presence of an additional parameter allows tuning the position of soliton.We find that the proposed scheme of bilinearization using auxiliary function,considerably simplifies the procedure yet generates a more general solutionthan the one reported earlier. We show that the obtained soliton solutionreduces to an algebraic soliton in the limit of infinite width. Further we showexplicitly that the soliton interactions are elastic through asymptoticanalysis, that is the amplitude of each soliton remains same before and afterinteraction. The mark of interaction is left behind only in the phase of eachsoliton. Secondly, we propose a generalised Lax pair for the FLE and obtain theconserved quantities by solving Riccati equation. We believe that the presentinvestigation would be useful to study the applications of FLE in nonlinearoptics and other branches of physics.

Bilinearization of the Fokas-Lenells equation Conservation laws and soliton interactions