Energy transfer mediated by Holstein-type interactions in two space dimensions.

Area of Science:

• Condensed matter physics
• Nonlinear dynamics
• Wave phenomena

Background:

• The Holstein approach models energy transfer in mechanical lattices.
• Understanding wave propagation and localization is crucial in various physical systems.

Purpose of the Study:

• To investigate the 2D energy transfer problem in a mechanical lattice with coupled interactions.
• To analyze the behavior of localized and traveling wave solutions.
• To determine the parameter regimes for wave localization and propagation.

Main Methods:

• Coupling of linear Schrödinger and sine-Gordon equations.
• Variational approach for parameter regime analysis.
• Newton method and pseudospectral method for numerical validation.

Main Results:

• Radially symmetric coupled localized and traveling solutions were found.
• A decreasing and oscillatory branch of solutions for wave function power was identified.
• An extended Vakhitov-Kolokolov stability criterion predicted bifurcation points.
• A critical ratio for interaction strengths was found for radial motion.

Conclusions:

• The interplay of interactions leads to stable, propagating wave solutions.
• The study provides a framework for understanding stable wave localization and motion in 2D lattices.
• Numerical validation confirmed the theoretical predictions for steady-state and moving cases.