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。此次有资格被提名的对象是2012年及之后获得博士学位的青年学者，他们被认为是相关领域表现最突出的新一代研究学者。 

　　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