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可積系統及相關領域的交叉研究(常向科)
2021-07-07 | 编辑:

  常向科副研究員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型可積方程非光滑孤子相關的重要問題,首次發現了具有Pfaffian結構的非光滑孤子系統,提出了部分斜正交多項式的新概念,提出了幾個新型有效的可積算法,揭示了兩類重要隨機矩陣系綜和可積系統的聯系等。因具有獨特的內在結構,可積系統與諸多數學、物理分支等的交叉研究可産生良好的交叉融合、相互促進作用。 

  常向科副研究員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.》的特別專輯“Emerging talent 2021”計劃。此計劃是爲了給數學物理相關領域中,處于早期職業階段的最佳研究學者提供展示平台,最終入選者由編委會成員提名産生。此次有資格被提名的對象是2012年及之後獲得博士學位的青年學者,他們被認爲是相關領域表現最突出的新一代研究學者。 

    

    

  相關論文:

  【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 

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