姓名：李若梦

职务/职称：副教授

研究领域：可积系统及应用

邮箱：liruomeng@zzu.edu.cn

简要经历

李若梦，副教授、硕士生导师。2018年毕业于郑州大学数学与统计学院获理学博士学位，主要从事可积系统及应用研究，在国内外重要学术期刊《Journal of Nonlinear Science》《Studies in Applied Mathematics》《Zeitschrift für angewandte Mathematik und Physik》等发表论文二十余篇，多篇论文入选ESI数据库被引前0.1%的热点论文、前1%的高被引论文。获河南省自然科学优秀学术论文一等奖、二等奖。

研究方向

当前的研究兴趣为孤子方程振荡精确解的求解和数值模拟。以水波和电磁波为代表的各种波在传播时，其能量通常会均匀地分散到四面八方，因此其振幅最终会衰减到零。在特殊的情况下有一类孤立波（称作孤立子或孤子），其能量可以沿一个方向稳定传播、不耗散。可积系统这一数学工具即是围绕这一现象逐步发展起来的，其目的是研究孤子方程（一种偏微分方程）的精确解、长时间渐近等性质。振荡精确解研究的是在不断波动的背景（区别于常数背景，即背景波的振幅是个常数）下非线性波的精确表示。学习可积系统需要掌握《数学分析》《复变函数》等课程，并熟悉Mathematica和MATLAB等数学软件。

主要项目

主持国家自然科学基金青年项目：多分量孤子方程的Darboux变换：Riccati方程和Baker-Akhiezer函数方法。

主持河南省青年人才托举工程项目：多分量可积方程一般达布变换的构造方法和怪波解。

奖励

1、指导学生获得2021年全国大学生数学建模竞赛国家二等奖

其他

2、主持郑州大学校级教改项目“新工科教育模式下《概率论与数理统计》课程教学改革研究与探索”。

论文

[1]Xianguo Geng, Jia Wang, Kedong Wang,李若梦.Soliton resolution for the complex short-pulse positive flow with weighted Sobolev initial data in the space-time soliton regions.Journal of Differential Equations. 386 (2024) 214-268.

[2] Xianguo Geng, Wenhao Li,李若梦. Long-time asymptotics for the coupled complex short-pulse equation with decaying initial data. Journal of Differential Equations. 386 (2024) 113-163.

[3] Feiying Yan, Xianguo Geng,李若梦. Spectral and soliton structures for the four-component Kaup-Newell type negative flow equation. Communications in Nonlinear Science and Numerical Simulation 126 (Early access)

[4]李若梦, Yihao Li, Jingru Geng. Multi-fold Darboux transforms and interaction solutions of localized waves to a general vector mKdV equation. Nonlinear Dynamics. 111 (2023) 12525-12540.

[5]李若梦, Xianguo Geng. Rogue waves and breathers of the derivative Yajima-Oikawa long wave-short wave equations on theta-function backgrounds. Journal of Mathematical Analysis and Applications. 527 (2023) 127399.

[6]李若梦, Jingru Geng, Xianguo Geng. Rogue-wave and breather solutions of the Fokas-Lenells equation on theta-function backgrounds. Applied Mathematics Letters. 142 (2023) 108661.

[7]李若梦，Xianguo Geng. Periodic-background solutions of Kadomtsev-Petviashvili I equation. ZeitschriftfürangewandteMathematikund Physik.74 (2023) 68.

[8] Kedong Wang, Xianguo Geng, Mingming Chen,李若梦. Spectral analysis and long-time asymptotics of a coupled nonlinearSchrödinger system. Bulletin of the Malaysian Mathematical Sciences Society. 45 (2022) 2071-2106.

[9]李若梦, Xianguo Geng. Periodic-background solutions for the Yajima-Oikawa long-wave-short-wave equation. Nonlinear Dynamics. 109 (2022) 1053-1067.

[10] Xianguo Geng,李若梦, Bo Xue. A vector Geng-Li model: New nonlinear phenomena and breathers on periodic background waves. Physica D–Nonlinear Phenomena. 434 (2022) 133270.

[11] Yihao Li, Xianguo Geng, Bo Xue,李若梦. Darboux transformation and exact solutions for a four-component Fokas-Lenells equation. Results in Physics. 31 (2021) 105027.

[12] Kedong Wang, Mingming Chen,李若梦, Xianguo Geng. An integrable generalized Korteweg-de Vries equation with pseudo-peakons. Applied Mathematics Letters. 115 (2021) 106942.

[13]李若梦, Xianguo Geng. A necessary and sufficient condition for the solvability of the nonlinear Schrodinger equation on a finite interval. Acta Mathematicae Applicatae Sinica – English Series. 37 (2021) 75-100.

[14]李若梦, Xianguo Geng. A matrix Yajima-Oikawa long-wave-short-wave resonance equation, Darboux transformations and rogue wave solutions. Communications in Nonlinear Science and Numerical Simulation. 90 (2020) 105408.

[15] Yihao Li,李若梦, Bo Xue, Xianguo Geng. A generalized complex mKdV equation: Darboux transformations and explicit solutions. Wave Motion. 98 (2020) 102639.

[16] Bo Xue, Huiling Du,李若梦. A five-component generalized mKdV equation and its exact solutions. Mathematics. 8 (2020)1145.

[17] Jia Wang, Ting Su, Xianguo Geng,李若梦. Riemann-Hilbert approach and N-soliton solutions for a new two-component Sasa-Satsuma equation. Nonlinear Dynamics. 101 (2020) 597-609.

[18] Xianguo Geng,李若梦, Bo Xue. A vector general nonlinear Schrödinger equation with (m plus n) components. Journal of Nonlinear Science. 30 (2020) 991-1013.

[19]李若梦, Xianguo Geng, Bo Xue. A generalization of the Landau-Lifschitz equation: breathers and rogue waves. Journal of Nonlinear Mathematical Physics. 27 (2020) 279-294.

[20]李若梦, Xianguo Geng. Rouge periodic waves of the sine-Gordon equation. Applied Mathematics Letters. 102 (2020) 106147.

[21] Siqi Xu,李若梦, Xianguo Geng. Riemann-Hilbert method for the three-component Sasa-Satsuma equation and its N-soliton solutions. Reports on Mathematical Physics. 85 (2020) 77-103.

[22] Kedong, Wang, Xianguo Geng, Mingming Chen,李若梦. Long-time asymptotics for the generalized Sasa-Satsuma equation. AIMS Mathematics. 5 (2020) 7413-7437.

[23]李若梦, Xianguo Geng. On a vector long wave-short wave model. Studies in Applied Mathematics. 144 (2020) 164-184.

[24]李若梦, Xianguo Geng, Bo Xue. Darboux transformations for a matrix long-wave-short-wave equation and higher-order rational rogue-wave solutions. Mathematical Methods in the Applied Sciences. 43 (2020) 948-967.

[25] Xianguo Geng,李若梦. On a vector modified Yajima-Oikawa long-wave-short-wave equation. Mathematics. 7 (2019) 958.

[26] Xianguo Geng,李若梦. Darboux transformation of the Drinfeld-Sokolov-Satsuma-Hirota system and exact solutions. Annals of Physics. 361 (2015) 215-225.

[27] Xianguo Geng,李若梦, Bo Xue. A new integrable equation with peakons and cuspons and its bi-Hamiltonian structure. Applied Mathematics Letters. 46 (2015) 64-69.