A solution method for autonomous first-order algebraic partial differential equations

作者：Grasegger Georg; Lastra Alberto; Rafael Sendra J; Winkler Franz

来源：Journal of Computational and Applied Mathematics, 2016, 300: 119-133.

DOI：10.1016/j.cam.2015.12.030

• Partial differential equations
• Algebraic hypersurface
• Rational parametrization
• Complete solution

In this paper we present a procedure for solving first-order autonomous algebraic partial differential equations in an arbitrary number of variables. The method uses rational parametrizations of algebraic (hyper)surfaces and generalizes a similar procedure for first-order autonomous ordinary differential equations. In particular we are interested in rational solutions and present certain classes of equations having rational solutions. However, the method can also be used for finding non-rational solutions.

• 出版日期2016-7