Abstract
We introduce a ‘hybrid’ Cole–Hopf–Darboux transformation to relate the solutions of nonlinear and linear second-order differential equations and derive classification and sufficient condition for this correspondence. We explore physical applications of this correspondence to nonlinear oscillations, the Duffing equation and a nonlinear form of the Schrödinger equation for the nonrelativistic hydrogen atom. In addition, 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Physics A: Mathematical and Theoretical
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
