
Accession Number : ADA193306
Title : Hodograph Transformations on Linearizable Partial Differential Equations,
Corporate Author : CLARKSON UNIV POTSDAM NY DEPT OF MATHEMATICS AND COMPUTER SCIENCE
Personal Author(s) : Clarkson, P A ; Fokas, A S ; Ablowitz, M J
PDF Url : ADA193306
Report Date : Jan 1986
Pagination or Media Count : 55
Abstract : This paper develops an algorithmic method for transforming quasilinear partial differential equations of a certain form into semilinear equations. This crucially involves the use of hodograph transformations (i.e., transformations which involve the interchange of dependent and independent variables). Furthermore, we find the most general quasilinear equation of the above form which can be mapped via a hodograph transformation to a semilinear form. This algorithm provides a method for establishing whether a given quasilinear equation is linearizable; i.e., is solvable in terms of either a linear partial differential equation or of a linear integral equation. In particular, we use this method to show how the Painleve tests may be applied to quasilinear equations. This appears to resolve the problem that solutions of linearizable quasilinear partial differential equations typically have movable fractional powers and so do not directly pass the Painleve tests.
Descriptors : *PARTIAL DIFFERENTIAL EQUATIONS, *TRANSFORMATIONS(MATHEMATICS), *HODOGRAPHS, ALGORITHMS, EQUATIONS, INTEGRAL EQUATIONS, LINEAR ALGEBRAIC EQUATIONS, LINEAR DIFFERENTIAL EQUATIONS, LINEARITY
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE