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

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.

preprint2019arXivOpen access
Yi ZhaoEngui Fan
nlin.SI
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Open access2 authors1 topic
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Yi ZhaoEngui Fan

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