Welcome to our website!

Dun Zhao

Professor of Institute of Applied Mathematics.

Email:zhaod@lzu.edu.cn

Ph.D.University of Lanzhou University, 1998, Mathematics

Biography

Academic Degrees
Ph.D., University of Lanzhou University, 1998, Mathematics.
M.S., University of Lanzhou University, 1992, Mathematics.
B.S., University of Lanzhou University, 1989, Mathematics.
Academic Career
2007/04-Present	Professor
	School of Mathematics and Statistics, Lanzhou University 
2001/01-2007/03	Associate Professor
	School of Mathematics and Statistics, Lanzhou University
1995/06-2000/12	Assistant Professor
                  School of Mathematics and Statistics, Lanzhou University
2010/03-2010/08     visiting scholar
Institute of physics, Chinese academy of sciences
2007/03-2008/03     visiting scholar
Nantes University, France
1999/12-2002/01     postdoctoral research
                    Department of physics, Lanzhou University

Social experience

  • Teaching and guiding the situation of graduate students

  • Project results

  • Research interests

    My research focuses on the study of the models arising from quantum mechanics, especially equations from Bose-Einstein condensates and nonlinear optics.   I am interested in the existence of solutions and their asymptotic behavior for the elliptic and evolution Schrodinger equations, and also do some research on soliton theory.

    Publications

  • [1] K. Wang, D. Zhao, Optimal nonlinearity control of Schrodinger equation, Evol. Equ. Control Theory 7, 317–33 (2018).
    [2] Q. X. Wang, D. Zhao, Existence and mass concentration of 2D attractive Bose-Einstein condensates with periodic potentials, J. Differential Equations 262, 2684-2704 (2017).
    [3] Y. J. Zhang, Zhao, D. Zhao, W. X. Ma, A unified inverse scattering transformation for the local and nonlocal nonautonomous Gross-Pitaevskii equations, J. Math. Phys.58, 013505 (2017).
    [4] Q. X. Wang, D. Zhao, K. Wang, Existence of solutions to nonlinear fractional schrodinger equations with singular potentials, Electron. J. Differential Equations 2016, 1-19 (2016).
    [5] B. H. Feng, D. Zhao, Optimal bilinear control of Gross–Pitaevskii equations with Coulombian potentials, J. Diff. Eqn. 260, 2973–2993 (2016). 
    [6] B. H. Feng, D. Zhao, and C. Y. Sun, Homogenization for nonlinear Schrodinger equations with periodic nonlinearity and dissipation in fractional order spaces, Acta Mathematica Scientia 35, 567-582 (2015). 
    [7] D. Zhao, S. W. Song, L. Wen, Z. D. Li, H. G. Luo, and W.M. Liu,Topological defects and inhomogeneous spin patterns induced by the quadratic Zeeman effect in spin-1 Bose-Einstein condensates, Phys. Rev. A 91, 013619  (2015).
    [8]  B. H. Feng, D. Zhao, Global well-posedness for nonlinear Schrodinger equations with energy-critical damping, Elect. J. Differential Equations. 2015, 1–9 (2015).
    [9] Y. J. Zhang, D. Zhao, and H. G. Luo, Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrodinger equation, Ann. Phys. 350, 112-123 (2014).
    [10] B. H. Feng, D. Zhao, and P. Y. Chen, Optimal bilinear control of nonlinear Schrodinger equations with singular potentials, Nonlinear Anal. 107, 12-21 (2014).
    [11] B. H. Feng, D. Zhao, C. Y. Sun, On the Cauchy problem for the nonlinear Schrodinger equations with time-dependent linear loss/gain, J. Math. Anal. Appl.  416,   901-923 (2014).
    [12] B. H. Feng, D. Zhao, and C. Y. Sun, The limit behavior of solutions for the nonlinear Schrodinger equation including nonlinear loss/gain with variable coefficient,J. Math. Anal. Appl. 405, 240-251 (2013).
    [13] C. Y. Ding, D. Zhao, and H. G. Luo, Painleve integrability of two-component nonautonomous nonlinear Schrodinger equations, J. Phys. A: Math. Theor. 45, 115203 (2012).
    [14] D. Zhao, Y. J. Zhang, W. W. Lou, and H. G. Luo,AKNS hierarchy, Darboux transformation and conservation laws of the 1-D nonautonomous nonlinear Schrodinger equations,J. Math. Phys. 52, 043502 (2011).
    [15] D. Zhao, X. G. He, and H. G. Luo , Transformation from the nonautonomous to standard NLS equations, Eur. Phys. J. D 53, 213–216 (2009).
    [16] X. G. He,D. Zhao, L. Li and H. G. Luo,Engineering integrable onautonomous nonlinear Schrodinger equations, Phys. Rev. E 79, 056610 (2009).
    [17] H. G. Luo, D. Zhao, and X. G. He, Exactly controllable transmission of nonautonomous optical solitons, Phys. Rev. A 79, 063802 (2009).
    [18] D. Zhao, H. G. Luo and H.Y. Chai,Integrability of the Gross–Pitaevskii equation  with Feshbach resonance management, Phys. Lett. A 372, 5644–5650 (2008).
    [19] D. Zhao, S. J. Wang and Luo Hong-Gang,Differential Representations of SO(4) Dynamical Group, Commun. Theor. Phys. 50, 63-68 (2008).
    [20] X. L. Fan and D. Zhao, Regularity of quasi-minimizers of integral functionals with discontinuous -growth conditions, Nonlinear Anal. 65, 1521—1531 (2006). 
    [21] X. L. Fan, Q. H. Zhang and D. Zhao, Eigenvalues of p(x)-Laplacian Dirichlet problem,J. Math. Anal. Appl. 302, 306-317 (2005). 
    [22] D. Zhao, H. G. Luo, S. J. Wang and W. Zuo, A direct truncation method for finding abundant exact solutions and application to the one-dimensional higher-order Schr?dinger equation, Chaos, Solitons and Fractals 24, 533–547 (2005).
    [23] D. Zhao and C.K. Zhong, Existence of local strong solutions of elliptic systems on unbounded domain, Inter. J. Diff. Eqns. & Appl. 7, 115-121 (2003).
    [24] S. J. Wang, C. L. Jia, D. Zhao, H. G. Luo and J. H.An,Dark and bright solitons in a quasi-one-dimensional Bose-Einstein Condensates,Phys. Rev. A 68, 015601 (2003).
    [25] S. J. Wang, D. Zhao, H. G. Luo, L. X. Cen and C. L. Jia,, Exact solution to the von Neumann equation of the quantum characteristic function of the two-level Jaynes-Cummings model, Phys. Rev. A 64, 052102 (2001).
    [26] X. L. Fan and D. Zhao, On the spaces L^{p(x)}(\Omega) and W^{m,p(x)}(\Omega) , J. Math. Anal. Appl. 263, 424-446 (2001).
    [27] X. L. Fan, J. S. Shen and D. Zhao, Sobolev embedding theorems for spaces W^{k,p(x)}(Omega), J. Math. Anal. Appl. 262, 749-760 (2001).
    [28] X. L., Fan , Y. Z. Zhao and D. Zhao , Compact imbedding theorems with symmetry of Strauss-Lions type for the space W^{1,p(x)}(Omega), J. Math. Anal. Appl. 255, 333-348 (2001).
    [29] X. L. Fan and D. Zhao , The quasi-minimizer of integral functionals with p(x)-growth conditions,Nonlinear Anal. 39, 807-816 (2000).
    [30] X. L. Fan and D. Zhao, A class of De Giorgi type and Holder continuity. Nonlinear Anal. 36, 295-318 (1999).
    
  • Honor and Award

  • Other information