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

作者：Cheng, Qiaoyuan; Fan, Engui^*

来源：Journal of Differential Equations, 2023, 366: 320-344.

DOI：10.1016/j.jde.2023.04.016

• Fokas-Lenells equation
• Cauchy problem
• Weighted Sobolev space
• Modified Darboux transformation
• Global well-posedness

In this paper, we prove the existence of global solutions in H3(R) boolean AND H2,1(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.

• 单位
  复旦大学