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Rational solutions for the equation of commutation of differential operators

✍ Scribed by P. G. Grinevich

Publisher
Springer US
Year
1982
Tongue
English
Weight
329 KB
Volume
16
Category
Article
ISSN
0016-2663

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When factoring linear partial differential systems with a finite-dimensional solution space or analysing symmetries of nonlinear ODEs, we need to look for rational solutions of certain nonlinear PDEs. The nonlinear PDEs are called Riccati-like because they arise in a similar way as Riccati ODEs. In

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Let K be a field of characteristic zero and M(Y ) = N a system of linear differential equations with coefficients in K(x). We propose a new algorithm to compute the set of rational solutions of such a system. This algorithm does not require the use of cyclic vectors. It has been implemented in Maple