A Generalized Cole-Hopf Transformation for Nonlinear ODES

2012/11/28 by Mayer Humi, Humi, Mayer
Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CA #math.MP

paper · pdf · doi:10.48550/arxiv.1211.6704

15 pages

arxiv created 2012/11/28 · arxiv updated 2012/11/29

Abstract

We introduce a hybrid Cole-Hopf-Darboux transformation to relate solutions of nonlinear and linear second order differential equations and derive a sufficient condition for this correspondence. In particular we show that solutions of some nonlinear second order equations are related to the special functions of mathematical physics through this transformation. These nonlinear equations can be viewed as the "class of special nonlinear equations" which correspond to the linear differential equations which define the special functions of mathematical physics.

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