Constructing Miura transformations using symmetry groups
Degree GrantorUniversity of Canterbury
Degree NameResearch report
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.
SubjectsField of Research::01 - Mathematical Sciences::0105 - Mathematical Physics
- Engineering: Reports