Translation:

Thesis:

Selected Papers:

Survey on Darboux transformation
• Z.X.Zhou: Darboux transformation for integrable systems with symmetries, Nonlinear Systems and Their Remarkable Mathematical Structures 3 (Eds. Euler R, Zhang DJ), CRC Press (2021), 201-226.

Darboux transformations for affine Toda equations

• Y.Y.Li and Z.X.Zhou: Exact solutions for two dimensional D_n⁽¹⁾ Toda equation, Commun. Nonl. Sci. Numer. Simul. (2024),107792. DOI: 10.1016/j.cnsns.2023.107792
• Z.X.Zhou: Darboux transformation and exact solutions for two dimensional A_2n-1⁽²⁾ Toda equations, Chinese Ann. Math. B43 (2022), 833-844.
• Z.X.Zhou: Darboux transformations for the Lax pairs related to two dimensional affine Toda equations (in Chinese), Sci. Sinica Math. 48 (2018), 869-878. DOI: 10.1360/N012017-00191
• Z.X.Zhou: Darboux transformations of lower degree for two dimensional C_l⁽¹⁾ and D_l+1⁽²⁾ Toda equations, Inverse Problems 24 (2008), 045016.
• Z.X.Zhou: Darboux transformations for some two dimensional affine Toda equations, Proceedings of the 4th International Congress of Chinese Mathematicians III, Higher Education Press (2008), 405-416 .
• Z.X.Zhou: Finite dimensional integrable systems related with two dimensional A_2l⁽²⁾, C_l⁽¹⁾ and D_l+1⁽²⁾ Toda equations, J. Geom. Phys. 57 (2007), 1037-1053.
• Z.X.Zhou: Darboux transformations and exact solutions of two-dimensional C_l⁽¹⁾ and D_l+1⁽²⁾ Toda equations, J. Phys. A 39 (2006), 5727-5737.
• Z.X.Zhou: Darboux transformations and exact solutions of two dimensional A_2n⁽²⁾ Toda equation, J. Math. Phys. 46 (2005), 033515.

Darboux transformatins for PT-symmetric problems

• Y.Y.Li and Z.X.Zhou: Dromion solutions of PT-symmetric (x,y)-nonlocal Davey-Stewartson I equation, Commun. Nonl. Sci. Numer. Simul. (2021), 105967. DOI: 10.1016/j.cnsns.2021.105967
• Z.X.Zhou: Darboux transformations and global explicit solutions for nonlocal Davey-Stewartson I equation, Stud. Appl. Math. 141 (2018), 186-204.
• Z.X.Zhou: Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrodinger equation, Commun. Nonl. Sci. Numer. Simul. 62 (2018), 480-488.

Constraint from higher dimentions to lower dimensions

• Z.X.Zhou: Finite dimensional Hamiltonian system related to a Lax pair with symplectic and cyclic symmetries, Nonlinearity 25 (2012), 371–396.
• Z.X.Zhou: Relation between hyperbolic Nizhnik-Novikov-Veselov equation and stationary Davey-Stewartson II equation, Inverse Problems 25 (2009), 025003.
• Z.X.Zhou: Finite dimensional Hamiltonians and almost-periodic solutions for 2+1 dimensional three-wave equations, J. Phys. Soc. Jpn. 71 (2002), 1857-1863.
• Z.X.Zhou: Liouville integrability of the finite dimensional Hamiltonian systems derived from principal chiral field, J. Math. Phys. 43 (2002), 5002-5012.
• Z.X.Zhou, W.X.Ma and R.G.Zhou: Finite-dimensional integrable systems associated with Davey-Stewartson I equation, Nonlinearity 14 (2001), 701-717.
• Z.X.Zhou and W.X.Ma: Finite dimensional integrable Hamiltonian systems associated with DSI equation by Bargmann constraints, J. Phys. Soc. Jpn. 70 (2001), 1241-1245.
• Z.X.Zhou: Localized solitons of hyperbolic su(N) AKNS system, Inverse Problems 14 (1998), 1371-1383.
• Z.X.Zhou: Nonlinear constraints and soliton solutions of 1+2 dimensional 3-wave equation, J. Math. Phys. 39 (1998), 986-997.
• Z.X.Zhou: Soliton solutions for some equations in 1+2 dimensional hyperbolic su(N) AKNS system, Inverse Problems 12 (1996), 89-109.
• Z.X.Zhou: Explicit solutions of N-wave equation in 1+2 dimensions, Phys. Lett. A168 (1992) 370-374.

Application of Darboux transformations in geometry and physics

• Z.X.Zhou: Relation between the solitons of Yang-Mills-Higgs fields in 2+1 dimensional Minkowski space-time and anti-de Sitter space-time, J. Math. Phys. 42 (2001), 4938-4946.
• Z.X.Zhou: Solutions of the Yang-Mills-Higgs equations in 2+1 dimensional anti-de Sitter space-time, J. Math. Phys. 42 (2001), 1085-1099.
• Z.X.Zhou: Darboux transformations for twisted so(p,q) system and local isometric immersion of space forms, Inverse Problems 14 (1998), 1353-1370.
• Z.X.Zhou: Construction of explicit solutions of modified principal chiral field in 1+2 dimensions via Darboux transformations, Differential Geometry, World Scientific (1993), 325-332.
• C.H.Gu and Z.X.Zhou: Explicit form of Backlund transformations for GL(N), U(N) and O(2N) principal chiral fields, Nonlinear evolution equations: integrability and spectral methods, Manchester University Press, 1990, 115-123.

General constructions of Darboux transformation and binary Darboux transformation

• Z.X.Zhou: Binary Darboux transformation for Manakov triad (II), Phys. Lett. A211 (1996), 191-198.
• C.H.Gu and Z.X.Zhou: On Darboux transformations for soliton equations in high dimensional space-time, Lett. Math. Phys. 32 (1994), 1-10.
• Z.X.Zhou: Binary Darboux transformation for Manakov triad, Phys. Lett. A195 (1994), 339-345.
• Z.X.Zhou: General form of nondegenerate Darboux matrices of first order for 1+1 dimensional unreduced Lax pairs, Chinese Mathematics into the 21st Century, Peking University Press (1991), 231-242.
• Z.X.Zhou: Determination of nondegenerate Darboux operators of first order in 1+2 dimensions, Nonlinear Physics, Springer-Verlag (1990), 23-28.
• Z.X.Zhou: On the Darboux transformation for 1+2 dimensional equations, Lett. Math. Phys. 16 (1988), 9-17.
• C.H.Gu and Z.X.Zhou: On the Darboux matrices of Backlund transformations for the AKNS system, Lett. Math. Phys. 13 (1987), 179-187.