Algebro-geometric solutions and their reductions for the Fokas-Lenells hierarchy

Abstract

This paper is dedicated to provide theta function representations of algebro-geometric solutions for the Fokas-Lenells (FL) hierarchy through studying an algebro-geometric initial value problem. Further, we reduce these solutions into $N$-dark solutions through the degeneration of associated Riemann surfaces.

48 pages. arXiv admin note: text overlap with arXiv:nlin/0702058, arXiv:nlin/0105021, arXiv:nlin/0611055 by other authors