张大军


98B6


职务/职称：教授

电子邮箱：djzhang AT staff.shu.edu.cn


研究领域：

孤立子与可积系统: 数学结构与精确解. 目前主要研究离散可积系统与椭圆函数。

教育经历：

1990-1994, 河北师范大学数学系，学士

1994-1997, 上海大学数学系，计算数学硕士

1998-2002, 上海大学数学系，博士

工作经历：

03/1997-05/1999, 助教, 上海大学数学系

06/1999-04/2003, 讲师, 上海大学数学系

05/2003-08/2007, 副教授, 上海大学数学系

09/2007-, 教授, 上海大学数学系

代表性科研项目：(*为主持)

  1. *国家自然科学基金（面上项目）:  高维离散可积系统和约化, No. 12271334, 01/2023-12/2026. 45万元.

  2. *国家自然科学基金（数学天元基金项目）：可积离散与近可积系统,  No. 12126352, 01/2022-12/2022, 20万元.

  3. *上海市“科技创新行动计划”“一带一路”国际合作项目: 特殊多项式与离散Painlevé方程,  No.20590742900, 10/2020-09/2023. 30万元.

  4. *国家自然科学基金（面上项目）:  具有特殊势的非线性薛定谔型方程, No. 11875040, 01/2019-12/2022.  60万元.

  5. (参加)国家自然科学基金（重点项目）:  非线性可积系统的几何结构与奇性分析, No. 11631007, 01/2017-12/2021,  （主持人：屈长征），54/230万元.

  6. *国家自然科学基金（面上项目）:  离散可积系统与椭圆函数, No. 11371241, 01/2014-12/2017. 55万元.

  7. *教育部博士点基金:  多元多维相容系统及其数学结构, No. 20113108110002, 01/2012-12/2015.  12万元.

  8. *国家自然科学基金（面上项目）:  多维相容系统的反散射理论, No. 11071157, 01/2011-12/2013.  26万元.

  9. *上海市科委白玉兰基金(with  Jarmo Hietarinta): 多维相容系统的精确解. 05/2008-04/2009.  3万元.

  10. *上海市科委白玉兰基金(with  Jarmo Hietarinta): 差分系统的可积性研究. 03/2006-02/2007.  2万元.

  11. *国家自然科学基金（面上项目）:  离散系统的可积特征与新解, No. 10671121, 01/2007-12/2009.  19万元.

  12. *上海市教委优秀青年教师后备人选基金:  非等谱发展方程, 09/2004-08/2006. 6万元.

  13. *国家自然科学基金（面上项目）:  孤子系统的新解与元胞自动机, No. 10371070, 01/2004-12/2006.  17万元.

  14. *上海市教委青年基金:  离散的孤子系统, No. 03AQ90, 10/2003-09/2005. 3万元.

代表性学术论文(自2013年)：

  1. Shangshuai Li, Changzheng  Qu, D-j Zhang, Solutions to the SU(N) self-dual Yang--Mills equation,  Physica D, 453 (2023) No.133828 (17pp). arxiv: 2211.08574.

  2. Frank W. Nijhoff, Ying-ying  Sun, D-j Zhang, Elliptic solutions of Boussinesq type lattice equations  and the elliptic Nth root of unity, Communications in Mathematical Physics,  399(2) (2023) 599-650. Doi: 10.1007/s00220-022-04567-8

  3. D-j Zhang, Shi-min Liu,  Xiao Deng, The solutions of classical and nonlocal nonlinear Schrödinger  equations with nonzero backgrounds: Bilinearisation and reduction approach,  Open Communications in Nonlinear Mathematical Physics, 3 (2023) 23-66.  arxiv: 2209.04826, https://doi.org/10.46298/ocnmp.10036

  4. Guesh Yfter Tela, Song-lin  Zhao, D-j Zhang, On the fourth-order lattice Gel’fand--Dikii equations,  SIGMA, 19 (2023) No.007 (30pp).

  5. Xing Li, D-j Zhang, Elliptic  soliton solutions: τ functions, vertex operators and bilinear identities,  Journal of Nonlinear Science, 32(5) (2022) No.70 (53pp).

  6. Shangshuai Li, Changzheng  Qu, Xiangxuan Yi, D-j Zhang, Cauchy matrix approach to the SU(2) self-dual  Yang--Mills equation, Stud. Appl. Math., 148(4) (2022) 1703-1721.

  7. Shu-zhi Liu, Jing Wang,  D-j Zhang, The Fokas-Lenells equations: Bilinear approach, Stud. Appl.  Math., 148(2) (2022) 651-688.

  8. Xiaoxue Xu, Cewen Cao, D-j  Zhang, Algebro-geometric solutions to the lattice potential modified  Kadomtsev–Petviashvili equation, J. Phys. A: Math. Theor., 55(37)  (2022) 375201 (28pp).

  9. Jarmo Hietarinta, D-j Zhang,  Discrete Boussinesq-type equations, in Nonlinear Systems and Their Remarkable  Mathematical Structures, Volume 3, Eds. Norbert Euler and Da-jun Zhang,  CRC Press, Taylor & Francis, Boca Raton, 2021, pp54-101. arXiv:2012.00495

  10. Aye Aye Cho, Maebel Mesfun,  D-j Zhang, A revisit to the ABS H2 equation, SIGMA, 17 (2021) No.093  (19pp).

  11. Danda Zhang, D-j Zhang,  Peter H. van der Kamp, From auto-Bäcklund transformations to auto-Bäcklund  transformations, and torqued ABS equations, Mathematical Physics, Analysis  and Geometry. 24 (2021) No.33 (23pp).

  12. Kui Chen, Cheng Zhang,  D-j Zhang, Squared eigenfunction symmetry of the DΔmKP hierarchy and  its constraint, Stud. Appl. Math., 147 (2021) 752-91.

  13. Shangshuai Li, Frank W.  Nijhoff, Ying-ying Sun, D-j Zhang, Symmetric discrete AKP and BKP equations,  J. Phys. A: Math. Theor., 54 (2021) 075201 (19pp).

  14. Danda Zhang, Peter H. van  der Kamp, D-j Zhang, Multi-component extension of CAC systems, SIGMA,  16 (2020) No.060 (30pp).

  15. Cheng Zhang, Linyu Peng,  D-j Zhang, Discrete Crum’s theorems and lattice KdV-type equations,  Theoretical and Mathematical Physics, 202(2), (2020) 165-182.

  16. Shi-min Liu, Hua Wu, D-j  Zhang, New results on the classical and nonlocal Gross-Pitaevskii equation  with a parabolic potential, Reports Math. Phys., 86(3) (2020) 271-92.

  17. Da-jun Zhang, Wronskian  solutions of integrable systems, in Nonlinear Systems and Their Remarkable  Mathematical Structures, Volume 2, Eds. N. Euler, M.C. Nucci, CRC Press,  Taylor & Francis, Boca Raton, 2020, pp415-44. arXiv: 1903.09283.

  18. Danda Zhang, D-j Zhang,  Addition formulae, Bäcklund transformations, periodic solutions and  quadrilateral equations, Front. Math. China, 14(1), (2019) 203-23.

  19. Kui Chen, Xiao Deng, Senyue  Lou, D-j Zhang, Solutions of nonlocal equations reduced from the AKNS  hierarchy, Stud. Appl. Math., 141 (2018) 113-41.  

  20. Danda Zhang, D-j Zhang,  Rational solutions to the ABS list: Transformation approach, SIGMA,  13 (2017) 078, 24 pp.

  21. Kui Chen, Xiao Deng, D-j  Zhang, Symmetry constraint of the differential-difference KP hierarchy  and a second discretization of the ZS-AKNS system, J. Nonl. Math. Phys.,  24: sup 1 (2017) 18-35.

  22. Ying-ying Sun, D-j Zhang,  F.W. Nijhoff, The Sylvester equation and the elliptic Korteweg-de Vries  system, J. Math. Phys., 58 (2017) 033504-25pp.

  23. Wei Fu, Zhijun Qiao, Junwei  Sun, D-j Zhang, Continuous correspondence of conservation laws of the  semi-discrete AKNS system, J. Nonlin. Math. Phys., 22(3) (2015) 321-41.

  24. D-j Zhang, Song-lin Zhao,  Ying-ying Sun, Jing Zhou, Solutions to the modified Korteweg-de Vries  equation (review), Rev. Math. Phys., 26(7, July14), (2014) No.1430006  (42pp).

  25. Dan-dan. Xu, D-j Zhang,  Song-lin Zhao, The Sylvester equation and integrable equations: I. The  Korteweg-de Vries system and sine-Gordon equation, J. Nonlin. Math.  Phys., 21, (2014), 382-406.

  26. Wei Fu, Lin Huang, K M  Tamizhmani, D-j Zhang, Integrability properties of the differential-difference  Kadomtsev-Petviashvili hierarchy and continuum limits, Nonlinearity,  26, (2013) 3197-229.

  27. D-j Zhang, Song-lin Zhao,  Solutions to ABS lattice equations generalized Cauchy matrix approach,  Stud. Appl. Math, 131(July) (2013) 72-103.

  28. Jarmo Hietarinta, D-j Zhang,  Hirota's method and the search for integrable partial difference equations.  1. Equations on a 3X3 stencil, J. Difference Equa. Appl., 19(8), (2013)  1292-316.

  29. D-j Zhang, Jun-wei Cheng,  Ying-ying Sun, Deriving conservation laws for ABS lattice equations  from Lax pairs, J. Phys. A: Math. Theore., 46, (2013) No. 265202 (19pp).


学术兼职：

  • Open Communications in Nonlinear  Mathematical Physics, March 2021-

  • Journal of Physics A: Mathematical  and Theoretical, Jan 2020 –

  • Journal of Nonlinear Mathematical  Physics, March 2016 – September 2020

  • Conference SIDE (Symmetries  and Integrability of Difference Equations),   member of the steering committee (from 2012), http://www.side-conferences.net


最后更新日期：2023.10.22

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