Li, Ziming; Schwarz, Fritz Rational solutions of Riccati-like partial differential equations. (English) Zbl 0985.34007 J. Symb. Comput. 31, No. 6, 691-716 (2001). The rational solutions to Riccati-like partial differential equations (for Riccati equations [see W. T. Reid, Riccati differential equations, New York-London: Academic Press (1972; Zbl 0254.34003)]) are considered. These systems arise in a similar way as Riccati ODEs. The structure of rational solutions is obtained, and an algorithm, called RationalSolution (it consists of 5 steps), for finding rational solutions to an associated Riccati-like system is given. As an application of the results obtained, the RationalSolution algorithm is applied to find all rational solutions to Lie’s system \[ \begin{gathered} \partial_xu+u^2+a_1u+a_2v+a_3=0,\quad\partial_xv+uv+c_1u+c_2v+c_3=0,\\ \partial_yu+uv+b_1u+b_2v+b_3=0,\quad\partial_yv+v^2+d_1u+d_2v+d_3=0, \end{gathered} \] where \(a_k,b_k,c_k,d_k\) are rational functions of \(x,y\) and hyperexponential solutions to linear homogeneous differential systems with finite linear dimension in several unknowns. Reviewer: Valery V.Karachik (Tashkent) Cited in 1 ReviewCited in 4 Documents MSC: 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 35C05 Solutions to PDEs in closed form 34A05 Explicit solutions, first integrals of ordinary differential equations 65D15 Algorithms for approximation of functions 68W30 Symbolic computation and algebraic computation 35G20 Nonlinear higher-order PDEs Keywords:nonlinear PDEs; Riccati equation; coherent system; second-order ordinary differential equations; rational function; algorithm; differential polynomials Citations:Zbl 0254.34003 Software:ALLTYPES PDFBibTeX XMLCite \textit{Z. Li} and \textit{F. Schwarz}, J. Symb. Comput. 31, No. 6, 691--716 (2001; Zbl 0985.34007) Full Text: DOI Link References: [1] Bajaj, C.; Canny, J.; Garrity, T.; Warren, J., Factoring rational polynomials over the complex numbers, SIAM J. 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