A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators

Abstract

We explore a nonlocal connection between certain linear and nonlinear ordinary differential equations (ODEs), representing physically important oscillator systems, and identify a class of integrable nonlinear ODEs of any order. We also devise a method to derive explicit general solutions of the nonlinear ODEs. Interestingly, many well-known integrable models can be accommodated into our scheme and our procedure thereby provides further understanding of these models.