English

Closed form Solutions to Some Nonlinear equations by a Generalized Cole-Hopf Transformation

Mathematical Physics 2014-07-22 v1 math.MP

Abstract

In the first part of this paper we linearize and solve the Van der Pol and Lienard equations with some additional nonlinear terms by the application of a generalized form of Cole-Hopf transformation. We then show that the same transformation can be used to linearize Painleve III equation for certain combinations of its parameters. Finally we linearize new forms of Burger's and related convective equations with higher order nonlinearities.

Keywords

Cite

@article{arxiv.1407.5331,
  title  = {Closed form Solutions to Some Nonlinear equations by a Generalized Cole-Hopf Transformation},
  author = {Mayer Humi},
  journal= {arXiv preprint arXiv:1407.5331},
  year   = {2014}
}

Comments

The paper is a merger of arXiv:1308.5965 and arXiv:1308.0858 with a new section in which I apply the generalized Cole-Hopf transformation to find analytical solutions to Painleve III equation

R2 v1 2026-06-22T05:08:28.790Z