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

TL;DR

This paper introduces a method using nonlocal transformations to identify and solve integrable complex nonlinear oscillator systems, linking them to linear ODEs for explicit solutions.

Contribution

It presents a novel approach to determine integrability of complex nonlinear oscillators and constructs their solutions via nonlocal transformations, expanding analytical tools in nonlinear dynamics.

Findings

Identified classes of integrable complex nonlinear oscillators.

Constructed explicit solutions for several physically relevant cases.

Established a connection between nonlinear and linear ODEs through nonlocal transformations.

Abstract

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.