English

A Generalized Cole-Hopf Transformation for Nonlinear ODES

Mathematical Physics 2012-11-29 v1 Classical Analysis and ODEs math.MP

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.

Keywords

Cite

@article{arxiv.1211.6704,
  title  = {A Generalized Cole-Hopf Transformation for Nonlinear ODES},
  author = {Mayer Humi},
  journal= {arXiv preprint arXiv:1211.6704},
  year   = {2012}
}

Comments

15 pages

R2 v1 2026-06-21T22:45:41.033Z