Constructing Miura transformations using symmetry groups

Type of content
Journal Article
Publisher's DOI/URI
Thesis discipline
Degree name
Research Report
Publisher
University of Canterbury. Dept. of Mathematics
Journal Title
Journal ISSN
Volume Title
Language
Date
1993
Authors
Guthrie, G. A.
Abstract

Generalizations of the Hopf-Cole transformation are constructed for any differential equation. Each non-conjugate continuous symmetry group of a differential equation generates a different transformation. When the symmetry group acts nonlocally the transformations obtained generalize the Miura and Bäcklund transformations. A new technique for constructing auto-Bäcklund transformations is described. This method is used to discover a new auto-Bäcklund transformation for the Harry Dym equation.

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Citation
Keywords
Ngā upoko tukutuku/Māori subject headings
ANZSRC fields of research
Field of Research::01 - Mathematical Sciences::0105 - Mathematical Physics
Rights
Copyright Graeme Alexander Guthrie