Invariance of Painlev property for some reduced (1+1)-dimensional equations

We study the Painleve′property of the (1+1)-dimensional equations arising from the symmetry reduction for the (2+1)-dimensional ones.Firstly,we derive the similarity reduction of the (2+1)-dimensional potential Calogero–Bogoyavlenskii–Schiff (CBS)equation and Konopelchenko–Dubrovsky (KD)equations with the optimal system of the admitted onedimensional subalgebras.Secondly,by analyzing the reduced CBS,KD,and Burgers equations with Painleve′test,respectively,we find both the Painleve′integrability,and the number and location of resonance points are invariant,if the similarity variables include all of the independent variables.     

Invariance of Painlev6 property for some reduced （1 ＋ 1）-dimensional equations

We study the Painlevé property of the （1＋1）-dimensional equations arising from the symmetry reduction for the （2＋1）- dimensional ones. Firstly, we derive the similarity reduction of the （2＋1）-dimensional potential Calogero-Bogoyavlenskii- Schiff （CBS） equation and Konopelchenko-Dubrovsky （KD） equations with the optimal system of the admitted one-dimensional subalgebras. Secondly, by analyzing the reduced CBS, KD, and Burgers equations with Painlevé test, re-spectively, we find both the Painlevé integrability, and the number and location of resonance points are invariant, if the similarity variables include all of the independent variables.     

离散晶格的正族、负族及其Hamilton结构

构造了一个新的等谱问题，利用相容性条件，推导出离散晶格方程的正族和负族。再利用迹恒等式，建立其Hamilton 结构。获得的离散方程族的达布变换、双线性化、对称、守恒率及其精确解也值得进一步研究。