| Riemann-Hilbert problem for the fifth-order modified Korteweg–de Vries equation with the prescribed initial and boundary values |
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| 作者姓名： | Beibei Hu Ling Zhang Ji Lin Hanyu Wei |
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| 作者单位： | 1. Department of Physics, Zhejiang Normal University;2. School of Mathematics and Finance, Chuzhou University;3. College of Mathematics and Statistics, Zhoukou Normal University |
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| 基金项目： | supported by the National Natural Science Foundation of China under Grant Nos. 12147115 and 11835011；;the Natural Science Foundation of Anhui Province under Grant No. 2108085QA09；;the University Natural Science Research Project of Anhui Province under Grant No. KJ2021A1094；;China Postdoctoral Science Foundation under Grant No. 2022M712833；;the Program for Science and Technology Innovation Talents in Universities of Henan Province under Grant No. 22HASTIT019；;the Natural Science Foundation of Henan Province under Grant No. 202300410524； |
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| 摘 要： | In this paper, we investigate the fifth-order modified Korteweg–de Vries(mKdV) equation on the half-line via the Fokas unified transformation approach. We show that the solution u(x, t) of the fifth-order m Kd V equation can be represented by the solution of the matrix Riemann-Hilbert problem constructed on the plane of complex spectral parameter θ. The jump matrix L(x, t, θ) has an explicit representation dependent on x, t and it can be represented exactly by the two pairs of spectral functions...
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