440 research outputs found
The Riemann-Hilbert approach for the integrable fractional Fokas--Lenells equation
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 -soliton solution in determinant form.
Additionally, we prove the fractional one-soliton solution rigorously. Notably,
we demonstrate that as , the fractional -soliton solution can
be expressed as a linear combination of fractional single-soliton
solutions
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