A nonlocal connection between certain linear and nonlinear ordinary differential equations – Part II: Complex nonlinear oscillators

•We identified a class of integrable nonlinear complex ODEs.•Two types of nonlocal transformations which connect the nonlinear complex ODE with linear ODE are presented.•General solution of a class of nonlinear complex ODEs are given.

In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear complex ordinary differential equations (ODEs) with complex linear ODEs, thereby proving the integrability of the former. We also show how to construct the solutions using the two types of nonlocal transformations with several physically interesting cases as examples.