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Rational Solutions of Riccati-like Partial Differential Equations

✍ Scribed by Ziming Li; Fritz Schwarz

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
436 KB
Volume
31
Category
Article
ISSN
0747-7171

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✦ Synopsis

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 this paper we describe the structure of rational solutions of a Riccati-like system, and an algorithm for computing them. The algorithm is also applicable to finding all rational solutions of Lie's system {βˆ‚xu

where a 1 , . . . , d 3 are rational functions of x and y.

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