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作 者:Ning ZHANG Tie-cheng XIA En-gui FAN
机构地区:[1]Department of Basical Courses, Shandong University of Science and Technology, Taian 271019, China [2]Department of Mathematics, Shanghai University, Shanghai 200444, China [3]School of Mathematical Sciences, Fudan University, Shanghai 200433, China
出 处:《Acta Mathematicae Applicatae Sinica》2018年第3期493-515,共23页应用数学学报(英文版)
基 金:Supported by the National Natural Science Foundation of China(No.11271008,61072147,11671095);SDUST Research Fund(No.2018TDJH101)
摘 要:In this paper, the Fokas unified method is used to analyze the initial-boundary value for the ChenLee-Liu equation i?tu + ?xxu-i|u2|?xu = 0 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.In this paper, the Fokas unified method is used to analyze the initial-boundary value for the ChenLee-Liu equation i?tu + ?xxu-i|u2|?xu = 0 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.
关 键 词:Chen-Lee-Liu equation initial-value problem RiemannIHilbert problem Fokas unified method jump matrix
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