研究方向:
(1)Riemann-Hilbert方法在可积方程中的应用,包括精确解的构造以及解的渐近性态分析;
(2)可积系统与其他方向的交叉,比如正交多项式、随机矩阵、Hurwitz数。
个人简介:
2007年9月至2017年7月在郑州大学数学与统计学院学习,2017年9月入职,2023年获河南省自然科学奖一等奖(4/6)。
科研项目:
(1)国家自然科学基金面上项目,Riemann-Hilbert 方法在具有非零边界的耦合可积方程的若干应用研究, 2022/01-2025/12, 主持;
(2)国家自然科学基金青年科学基金项目,一类可积方程的渐近分析,2019/01-2021/12,主持。
代表性论文:
(1) Huan Liu*, Jing Shen, Xianguo Geng, Inverse scattering transformation for the N-component focusing nonlinear Schrödinger equation with nonzero boundary conditions, Letters in Mathematical Physics, 2023, 113:23.
(2) Huan Liu*, Xianguo Geng, Bo Xue, The Deift-Zhou steepest descent method to long-time asymptotics for the Sasa-Satsuma equation, Journal of Differential Equations, 2018, 265(11): 5984-6008.
(3) Xianguo Geng, Huan Liu*, The nonlinear steepest descent method to long-time asymptotics of the coupled nonlinear Schrödinger equation, Journal of Nonlinear Science, 2018, 28(2): 739-763.
(4) Huan Liu*, Xianguo Geng, The vector derivative nonlinear Schrödinger equation on the half-line, IMA Journal of Applied Mathematics, 2018, 83(1):148-173.
(5) Huan Liu*, Xianguo Geng, Initial-boundary problems for the vector modified Korteweg-de Vries equation via Fokas unified transform method, Journal of Mathematical Analysis and Applications, 2016, 440(2): 578-596.
(6) Xianguo Geng, Huan Liu*, Junyi Zhu, Initial-boundary value problems for the coupled nonlinear Schrödinger equation on the half-Line, Studies in Applied Mathematics, 2015, 135(3): 310-346.