Skip to main content
padlock icon - secure page this page is secure

Symmetry Analysis of Abel's Equation

Buy Article:

$59.00 + tax (Refund Policy)

A solution algorithm for Abel's equation and some generalizations based on a nontrivial Lie symmetry of a particular kind, i.e., so-called structure-preserving symmetry, is described. For the existence of such a symmetry a criterion in terms of the coefficients of the so-called rational normal form of the given equation is derived. If it is affirmative, solving Abel's equation is reduced to a well-defined integration problem. It is shown that almost all known ad hoc methods for obtaining closed form solutions are consequences of this type of symmetry. Possible extensions of this scheme to more general classes of first-order ordinary differential equations are pointed out.
No References
No Citations
No Supplementary Data
No Article Media
No Metrics

Document Type: Research Article

Affiliations: GMD, Institut SCAI

Publication date: April 1, 1998

  • Access Key
  • Free content
  • Partial Free content
  • New content
  • Open access content
  • Partial Open access content
  • Subscribed content
  • Partial Subscribed content
  • Free trial content
Cookie Policy
X
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more