Analytical homoclinic solution of a two dimensional nonlinear system of differential equations

TL;DR

This paper derives an analytical homoclinic orbit solution for a two-dimensional nonlinear differential system modeling the slow flow of a dissipative coupled oscillator system with nonlinear attachment.

Contribution

It provides the first explicit analytical solution for the homoclinic orbit in this specific nonlinear, dissipative, coupled oscillator system.

Findings

Explicit analytical homoclinic solution derived

Applicable to Hamiltonian part of slow flow in dissipative systems

Enhances understanding of nonlinear oscillator dynamics

Abstract

Analytical solution of the homoclinic orbit of a two dimensional system of differential equations that describes the hamiltonian part of the slow flow of a three degree of freedom dissipative system of linear coupled oscillators with an essentially nonlinear attachment.