2014/07/20 by Mayer Humi, Humi, Mayer
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1407.5331
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
arxiv created 2014/07/20 · arxiv updated 2014/07/22
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.