Rational general solutions of systems of first-order algebraic partial differential equations
2018
Abstract We study the rational solutions of systems of first-order algebraic partial differential equations and relate them to those of an associated autonomous system. We also describe how rational general solutions of these systems are related, and provide an algorithm in some particular case concerning the dimension of the associated algebraic variety. Our results can be considered as a generalization of the approach by L. X. C. Ngo and F. Winkler on algebraic ordinary differential equations of order one, adapted to systems of first-order algebraic partial differential equations.
Keywords:
- Mathematics
- Mathematical analysis
- Singular point of an algebraic variety
- Algebraic differential equation
- Real algebraic geometry
- Differential algebraic equation
- Function field of an algebraic variety
- Dimension of an algebraic variety
- Discrete mathematics
- Algebraic analysis
- Differential algebraic geometry
- Algebra
- Stochastic partial differential equation
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
28
References
5
Citations
NaN
KQI