Auxiliary functions for rational ODEs with 2 and 3 singular values

30th International Colloquium on Group Theoretical Methods in Physics

Filipuk, G.^1

Institute of Mathematics, University of Warsaw, ul. Banacha 2, Warsaw

02-097, Poland^1

关键词: Auxiliary functions;    First order;    Linear differential equation;    Nonlinear differential equation;    Painleve equations;    Second order nonlinear differential equation;    Singular values;    Suitable conditions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012036/pdf
DOI  :  10.1088/1742-6596/597/1/012036

来源: IOP

【 摘 要 】

We examine auxiliary functions which are related to certain second order nonlinear differential equations with 2 and 3 singular values. The auxiliary functions satisfy first order linear differential equations. It is shown that after imposing suitable conditions on the coefficients of the linear equations and on the form of the auxiliary functions one can reduce the nonlinear differential equations to the (modified) third and fifth Painleve equations and the fourth Painleve equation.