The Fokas-Lenells equation on the line: Global well-posedness with solitons.

In this paper, we prove the existence of global solutions in H 3 (R) ∩ H 2 , 1 (R) to the Fokas-Lenells (FL) equation on the line when the initial data includes solitons. A key tool in proving this result is a newly modified Darboux transformation, which adds or subtracts a soliton with given spectral and scattering parameters. In this way the inverse scattering transform technique is then applied to establish the global well-posedness of initial value problem with a finite number of solitons based on our previous results on the global well-posedness of the FL equation. [ABSTRACT FROM AUTHOR]