Solutions to Painleve III and other nonlinear equations by a generalized Cole–Hopf transformation |
| |
| Authors: | Mayer Humi |
| |
| Institution: | Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA |
| |
| Abstract: | In this paper, we introduce a generalized form of Cole‐Hopf transformation and apply it to find new closed‐form (analytic) solutions to Painleve III equation. The same transformation is used then to find analytic solutions for the van der Pol and other nonlinear convective equations. These solutions provide analytic insights to some practical problems and might be used also to test the accuracy of numerical solutions. Copyright © 2017 John Wiley & Sons, Ltd. |
| |
| Keywords: | Cole– Hopf transformation Painleve III equation convective equations |
|
|
