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- W2883861304 abstract "The solution of the initial value problem (IVP) for the Fokas–Lenells equation (FLE) was constructed in terms of the solution M ( x , t , k ) of a 2 × 2 matrix Riemann–Hilbert problem (RHP) as k → ∞ , and the one-soliton solution of the FLE was derived based on this Riemann–Hilbert problem, in Lenells and Fokas (2009). However, in fact, the derivative with respect to x of the solution of the FLE ( u x ( x , t ) ) was recovered from the RHP as k → ∞ . In this paper, we construct the solution of the FLE in terms of the RHP as k → 0 , because the Lax pair of the FLE contains the negative order of the spectral variable k . We show that the one-soliton solution of the FLE obtained in this paper is the same as Lenells and Fokas (2009), but avoiding a complex integral." @default.
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- W2883861304 date "2019-01-01" @default.
- W2883861304 modified "2023-10-18" @default.
- W2883861304 title "On a Riemann–Hilbert problem for the Fokas–Lenells equation" @default.
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- W2883861304 doi "https://doi.org/10.1016/j.aml.2018.07.027" @default.
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