This paper shows that explicit and exact general periodic solutions for various types of Lienard equations can be computed by applying the generalized Sundman transformation. As an il- lustration of the efficiency of the proposed theory, the cubic Duffing equation and Painleve- Gambier equations were considered. As a major result, it has been found, for the first time, that equation XII of the Painleve-Gambier classication can exhibit, according to an appropriate parametric choice, trigonometric solutions, but with a shift factor.
Comments: 12 pages
Unique-IP document downloads: 58 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.