Phase compactons in chains of dispersively coupled oscillators

Area of Science:

• Nonlinear dynamics
• Complex systems
• Wave phenomena

Background:

• Oscillatory systems are fundamental in physics and engineering.
• Understanding wave propagation and solitary waves is crucial for many applications.
• Previous models often simplify coupling mechanisms, limiting applicability.

Purpose of the Study:

• To investigate the phase dynamics of coupled autonomous oscillators.
• To analyze the behavior of solitary waves, specifically compactons and kovatons, in such systems.
• To explore the impact of different coupling types (dispersive vs. nondispersive) on these wave structures.

Main Methods:

• Derivation of a Korteveg-de Vries-like equation with nonlinear dispersion from a discrete oscillator model.
• Numerical simulations using the complex Ginzburg-Landau and Van der Pol lattices.
• Analysis of wave-wave and wave-kink interactions.

Main Results:

• The system supports compactons (solitary waves with compact support) and kovatons (bound kink-antikink pairs).
• These robust objects, along with wave trains, constitute the primary components of the system's dynamics.
• Nondispersive coupling affects compactons (damping, deceleration, or acceleration) but leaves kovatons largely unchanged.

Conclusions:

• The study reveals novel solitary wave solutions (compactons and kovatons) in coupled oscillator systems.
• The nature of coupling significantly influences the dynamics of compactons, highlighting the importance of nonlinear dispersion.
• Kovatons exhibit remarkable robustness against changes in coupling, suggesting their potential as stable information carriers.