[29] Yutong Qi, Zhiguo Xu, Wenlei Li, Shaoyun Shi, Quantized vortex dynamics in the Ginzburg-Landau equation on the disc domain based on the reduced dynamical law, Phys. D 490 (2026), Paper No. 135164.
[28] Sheng Chen, Guangshen Liu, Zhiguo Xu, Yong Zhang, Multidomain Fourier-Chebyshev spectral method for computing rogue waves in the nonlinear Schrödinger equation, J. Sci. Comput. 105 (2025), no. 2, Paper No. 42, 23 pp.
[27] Yongyong Cai, Yue Feng, Yichen Guo, Zhiguo Xu, Uniform and optimal error estimates of a nested Picard integrator for the nonlinear Schrödinger equation with wave operator, Numer. Methods Partial Differ. Equations, 40 (2024), no. 6, 1-32.
[26] Zhiguo Xu, Lin Xu, Wenlei Li Shaoyun Shi, Renormalization Group Method for Singular Perturbation Initial Value Problems with Delays, Mediterr. J. Math., 20 (2023), no. 73.
[25] Fangcheng Fan, Zhiguo Xu, Breather and rogue wave solutions for the generalized discrete Hirota equation via Darboux–Bäcklund transformation, Wave Motion, 119(2023), 103139.
[24] Fangcheng Fan, Zhiguo Xu, Shaoyun Shi, Soliton, breather, rogue wave and continuum limit for the spatial discrete Hirota equation by Darboux–Bäcklund transformation, Nonlinear Dyn., 111 (2023), no. 11, 10393-10405.
[23] Fangcheng Fan, Zhiguo Xu, Shaoyun Shi, N-fold Darboux transformation and soltion solutions for the relativistic Toda lattice equation, Rep. Math. Phys., 89 (2022), no. 1, 9-25.
[22] Yue Feng, Zhiguo Xu, Jia Yin, Uniform error bounds of exponential wave integrator methods for the long-time dynamics of the Dirac equation with small potentials, Appl. Numer, Math., 172(2022) 50-66.
[21] Zhiguo Xu, A generalized integrable hierarchy related to the relativistic Toda lattice: Hamiltonian structure, Darboux transformation, soliton solution and conservation law, Mod.Phys.Lett. B, Vol. 36,No. 02, 2150545 (2022).
[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.
[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.
[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.
[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.
[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.
[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.
