Hodograph Transformations on Linearizable Partial Differential Equations,
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1986
- Accession Number
- ADA193306
Entities
People
- A. S. Fokas
- M. J. Ablowitz
- P. A. Clarkson
Organizations
- Clarkson University