Inverse scattering transformation for the Fokas-Lenells equation with nonzero boundary conditions

2019/12/28 by Yi Zhao, Zhao, Yi, Engui Fan +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1912.12400

openalex publication_date 2019/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we focus on the inverse scattering transformation for the Fokas-Lenells (FL) equation with nonzero boundary conditions via the Riemann-Hilbert (RH) approach. Based on the Lax pair of the FL equation, the analyticity and symmetry, asymptotic behavior of Jost solutions and scattering matrix are discussed in detail. With these results, we further present a generalized RH problem, from which a reconstruction formula between the solution of the FL equation and the Riemann-Hilbert problem is obtained. The N-soliton solutions of the FL equation is obtained via solving the RH problem.

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