Abstract
In this paper, the Fokas unified method is used to analyze the initial-boundary value for the Chen- Lee-Liu equation
on the half line (−∞, 0] with decaying initial value. Assuming that the solution u(x, t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter λ. The jump matrix has explicit (x, t) dependence and is given in terms of the spectral functions {a(λ), b(λ)} and {A(λ), B(λ)}, which are obtained from the initial data u0(x) = u(x, 0) and the boundary data g0(t) = u(0, t), g1(t) = ux(0, t), respectively. The spectral functions are not independent, but satisfy a so-called global relation.
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Supported by the National Natural Science Foundation of China (No.11271008, 61072147, 11671095) and SDUST Research Fund (No.2018TDJH101).
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Zhang, N., Xia, Tc. & Fan, Eg. A Riemann-Hilbert Approach to the Chen-Lee-Liu Equation on the Half Line. Acta Math. Appl. Sin. Engl. Ser. 34, 493–515 (2018). https://doi.org/10.1007/s10255-018-0765-7
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DOI: https://doi.org/10.1007/s10255-018-0765-7