The Riemann-Hilbert approach for the integrable fractional Fokas-Lenells equation

摘要

In this paper, we propose a new integrable fractional Fokas-Lenells equation by using the completeness of the squared eigenfunctions, dispersion relation, and inverse scattering transform. To solve this equation, we employ the Riemann-Hilbert approach. Specifically, we focus on the case of the reflectionless potential with a simple pole for the zero boundary condition. And we provide the fractional N-soliton solution in determinant form. In addition, we prove the fractional one-soliton solution rigorously. Notably, we demonstrate that as |t|->infinity, the fractional N-soliton solution can be expressed as a linear combination of N fractional single-soliton solutions.

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