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许志国

发表于: 2017-11-30   点击: 


基本情况
姓名: 许志国
性别:
职称: 副教授
所在系别: 基础数学系
最高学历: 研究生
最高学位: 博士
Email: xuzg2014@jlu.edu.cn







详细情况


所在学科业:

基础数学

所研究方向:

微分方程与动力系统,可积系统,偏微分方程数值解

讲授课程:

常微分方程,常微分方程习题,动力系统,微积分,线性代数

教育经历:

200809-201107 吉林大学数学学院博士

200609-200807 吉林大学数学学院硕士

200209-200607 吉林大学数学学院学士

工作经历:

201610-至今  吉林大学数学学院副教授

201501-201509 新加坡国立大学数学系访问学者

201401-201609 吉林大学数学学院讲师

201107-201401 北京计算科学研究中心博士后

201112-201201 新加坡国立大学数学系访问学者

科研项目:

1. 科技创新2030-“新一代人工智能”重大课题项目,开放环境下安全可信人机共驾测试场景构建与验证平台——22021/01-2024/12, 在研,主持

2.吉林省自然科学基金学科布局,非线性涡旋系统的动力学研究,2020/01-2022/12, 在研,主持

3. 吉林省教育厅科学技术研究项目重点项目,Darboux 变换及其在可积系统中的应用,2021/01-2023/12, 在研,主持

4. 国家自然科学基金面上项目,多尺度问题额重整化群方法,2022/01-2025/12,在研,参与

5. 国家自然科学基金青年项目,非线性Schrödinger方程孤立子和怪波的数值方法,2016/01-2018/12,结题,主持。

6. 吉林省自然科学基金青年人才基金,一类非线性偏微分方程孤立子和怪波的分析与计算,2017/01-2018/12,结题,主持。

7. 吉林省教育厅科学技术研究项目,耦合非线性Schrödinger方程组孤立子的研究,2016/01-2018/12, 结题,主持。

学术论文:

[20] Lin Xu, Zhiguo Xu, Wenlei Li#, Shaoyun Shi, Renormalization group approach to a class of singularly perturbed delay differential equations, Commun. Nonlinear Sci. Numer. Simulat. 103(2021)106028

[19] Zhiguo Xu, Infinitely many solutions for the fractional p&q problem with critical Sobolev-Hardy exponents and sign-chaging weight functions, Differential and integral Equations (2021) Vol. 34, no.9-10, 519-537.

[18] FangCheng Fan, ShaoYun Shi, Zhiguo Xu#, Positive and negative integrable lattice hierarchies: conservation laws and N-fold Darboux transformations, Commun. Nonlinear Sci. Numer. Simulat. 91 (2020) 105453

[17] FangCheng Fan, ShaoYun Shi, Zhiguo Xu#, Conservation laws and Darboux transformations for a3-coupled integrable lattice equations. Modern Phys. Lett. B 34(2020) no. 21, 2050218, 12pp.

[16] Fangcheng Fan, Zhiguo Xu#, Shaoyun Shi, N-fold Darboux transformations and exact solutions of the combined Toda lattice and relativistic Toda lattice equation. Anal. Math. Phys. 10, 31(2020)  

[15] Pengde Wang; Zhiguo Xu#; Jia Yin, Simple high-order boundary conditions for computing rogue waves in the nonlinear Schrödinger equation.  Comput. Phys. Commun. 251 (2020), 107109, 13 pp.

[14] Fangcheng Fan, Shaoyun Shi, Zhiguo Xu#. A hierarchy of integrable differential-difference equations and Darboux transformation, Rep. Math. Phys., 84 (2019), No. 3, 289-301.

[13] Fangcheng Fan, Shaoyun Shi, Zhiguo Xu#. Infinite number of conservation laws and Darboux

transformations for a 6-field integrable lattice system, Int. J. Mod. Phys., 33 (2019) 1950147,16pp.

[12] Kaiyin Huang, Shaoyun Shi, Zhiguo Xu#. Integrable deformations, bi-Hamiltonian structures and nonintegrability of a generalized Rikitake system, Int. J. Geom. Methods Mod. Phys., 16 (2019), no. 4, 1950059, 17 pp.

[11] Zhiguo Xu, Weizhu Bao, Shaoyun Shi; Quantized vortex dynamics and interaction patterns in superconductivity based on the reduced dynamical law, Discrete Contin. Dyn. Syst. Ser. B, 23 (2018), No. 6, 2265-2297.

[10] Yongjun Yuan, Zhiguo Xu, Qinglin Tang, Hanquan Wang; The Numerical Study of the Ground States of Spin-1 Bose-Einstein Condensates with Spin-Orbit-Coupling, E.ASIAN. J. APPL. MATH., 8 (2018), No. 3, pp. 598-610.

[9] Zhiguo Xu, Wenlei Li, Shaoyun Shi; Higher order criterion for the nonexistence of formal first integral for nonlinear systems, Electron. J. Differential Equations, Vol. 2017 (2017), No. 274, pp. 1-11.(2017.11.5)(0.954)2019

[8] Zhiguo Xu, Xuanchun Dong, Yongjun Yuan, Error estimates in the energy space for a Gautschi-type integrator spectral discretization for the coupled nonlinear Klein-Gordon equations. J. Comput. Appl. Math. 292 (2016), 402–416.  (2016.01)1.328

[7] Hanquan Wang, Zhiguo Xu, Projection gradient method for energy functional minimization with a constraint and its application to computing the ground state of spin-orbit-coupled Bose-Einstein condensates. Comput. Phys. Commun. 185 (2014), no. 11, 2803–2808. (2014.11) (3.635)

[6] Xuanchun Dong, Zhiguo Xu; Xiaofei Zhao, On time-splitting pseudospectral discretization for nonlinear Klein-Gordon equation in nonrelativistic limit regime. Commun. Comput. Phys. 16 (2014), no. 2, 440–466. (2014.08)1.778

[5] Weizhu Bao, Qinglin Tang, Zhiguo Xu, Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation. J. Comput. Phys. 235 (2013), 423–445.  2013.02(2.566)

[4] Zhiguo Xu, Shaoyun Shi, Fang Liu, Nonexistence and partial existence of first integrals for diffeomorphisms. Appl. Math. Lett. 23 (2010), no. 4, 399–403.

[3] Wenlei Li, Zhiguo Xu#, Shaoyun Shi, Nonexistence of formal first integrals for nonlinear systems under the case of resonance. J. Math. Phys.51 (2010), no. 2, 022703, 11 pp.

[2] Jiao, Jia; Shi, Shaoyun; Xu, Zhiguo, Formal first integrals for periodic systems. J. Math. Anal. Appl. 366 (2010), no. 1, 128–136.

[1] Fang Liu, Shaoyun Shi, Zhiguo Xu#, Nonexistence of formal first integrals for general nonlinear systems under resonance. J. Math. Anal.363(2010), no. 1,214–219.


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