Nonlinear coupled-mode framework for coupled systems: From exact Hamiltonian models to improved reduced-order...

Area of Science:

• Physics
• Nonlinear Dynamics
• Circuit Theory

Background:

• Accurate modeling of coupled nonlinear phenomena is crucial for understanding energy transfer in physical systems.
• Conventional coupled-mode theory has limitations in moderate and strong coupling regimes due to approximations.

Purpose of the Study:

• Develop a nonlinear coupled-mode framework that systematically includes nonlinear interactions and counter-propagating wave effects.
• Improve the accuracy of reduced-order models for coupled nonlinear systems.

Main Methods:

• Derived a reduced-order formulation from an exact Hamiltonian description for nonlinear LC circuits with Josephson junctions.
• Incorporated essential nonlinear and self-coupling contributions, including rapidly oscillating terms.
• Performed comparative analysis against exact Hamiltonian dynamics.

Main Results:

• The proposed framework achieves quantitative agreement with exact Hamiltonian dynamics across weak-to-strong coupling regimes.
• Conventional coupled-mode models show significant phase and amplitude errors outside the weak-coupling regime.
• The new model overcomes limitations of traditional formulations.

Conclusions:

• Established a systematic pathway for constructing accurate reduced-order descriptions of coupled nonlinear systems.
• Clarified the limitations of existing phenomenological models.
• Findings have implications for circuit dynamics, photonics, and energy transfer in complex media.