常向科副研究员与合作者在可积系统与正交多项式、随机矩阵、数值算法等交叉研究方面取得了若干进展。例如，解决了多个Camassa-Hom型可积方程非光滑孤子相关的重要问题，首次发现了具有Pfaffian结构的非光滑孤子系统，提出了部分斜正交多项式的新概念，提出了几个新型有效的可积算法，揭示了两类重要随机矩阵系综和可积系统的联系等。因具有独特的内在结构，可积系统与诸多数学、物理分支等的交叉研究可产生良好的交叉融合、相互促进作用。
常向科副研究员的部分工作获得了国内外同行的高度认可与好评。他入选了国际期刊《J. Phys. A: Math. Theor.》的特别专辑“Emerging talent 2021”计划。此计划是为了给数学物理相关领域中，处于早期职业阶段的最佳研究学者提供展示平台，最终入选者由编委会成员提名产生。获得提名的研究学者是被认为最具有天赋的新一代研究学者，只有2012年之后获得博士学位的研究学者才有资格被提名。
相关论文：
【1】 B. Wang, X.K. Chang, X.B. Hu and S.H. Li. Discrete invariant curve flows, orthogonal polynomials and moving frame. to appear in Int. Math. Res. Not. DOI: 10.1093/imrn/rnz379
【2】 X.K. Chang, S.H. Li, S. Tsujimoto and G.F. Yu. Two-parameter generalizations of Cauchy bi-orthogonal polynomials and integrable lattices. J. Nonlinear Sci. 31: Paper No. 30, 23 pages, 2021？
【3】 X.K. Chang, X.B. Hu, J. Szmigielski and A. Zhedanov. Isospectral flows related to Frobenius-Stickelberger-Thiele polynomials. Commun. Math. Phys. 377, 387–419, 2020 ？
【4】 X.K. Chang and J. Szmigielski. Lax integrability and the peakon problem for the modified Camassa-Holm equation. Commun. Math. Phys. 358(1): 295–341, 2018
【5】 X.K. Chang, Y. He, X.B. Hu, and S.H. Li. Partial-skew-orthogonal polynomials and related integrable lattices with Pfaffian tau-functions. Commun. Math. Phys. 364(3): 1069–1119, 2018 ？
【6】 X.K. Chang, X.B. Hu, S.H. Li and J.X. Zhao. An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type. Adv. Math. 338:1077– 1118, 2018 ？
【7】 X.K. Chang, X.B. Hu, and S.H. Li. Degasperis-Procesi peakon dynamical system and finite Toda lattice of CKP type. Nonlinearity 31:4746–4775, 2018
【8】 X.K. Chang, X.B. Hu, and S.H. Li. Moment modification, multipeakons, and nonisospectral generalizations. J. Differ. Equations 265:3858–3887, 2018 ？
【9】 X.K. Chang, Y. He, X.B. Hu, and S.H. Li. A new integrable convergence acceleration algorithm for computing Brezinski-Durbin-Redivo-Zaglia’s sequence transformation via pfaffians. Numer. Algorithm. 78(1): 87–106, 2018
【10】S. Anco, X.K. Chang and J. Szmigielski. The dynamics of conservative peakons in a family of U(1)-invariant integrable equations of NLS-Hirota type. Stud. Appl. Math. 141: 680–713, 2018
【11】X.K. Chang, X.B. Hu and J. Szmigielski. Multipeakons of a two-component modified Camassa-Holm equation and the relation with the finite Kac-van Moerbeke lattice. Adv. Math. 299:1–35, 2016
【12】X.K. Chang, X.B. Hu and G. Xin. Hankel determinant solutions to several discrete integrable systems and the Laurent property. SIAM. J. Discrete Math. 29(1): 667–682, 2015
【13】X.M. Chen, X.K. Chang, J.Q. Sun, X.B. Hu and Y.N. Yeh. Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions. Nonlinearity 28(7):2279–2306, 2015？
【14】X.K. Chang, X.M. Chen and X.B. Hu. A generalized nonisospectral Camassa-Holm equation and its multipeakon solutions. Adv. Math. 263:154-177, 2014 ？
【15】J.Q. Sun, X.K. Chang, Y. He and X.B. Hu. An extended multistep Shanks transformation and convergence acceleration algorithm with their convergence and stability analysis. Numer. Math.125(4):785–809, 2013 ？
本文版权归原作者所有，文章内容不代表平台观点或立场。如有关于文章内容、版权或其他问题请与我方联系，我方将在核实情况后对相关内容做删除或保留处理！