Discrete breathers in Klein-Gordon lattices: A deflation-based approach

Area of Science:

• Nonlinear dynamics
• Numerical analysis
• Computational physics

Background:

• Deflation is a numerical technique for finding steady-state solutions to nonlinear partial differential equations.
• Identifying periodic orbits in nonlinear dynamical lattices is crucial for understanding complex system behavior.

Purpose of the Study:

• To extend the deflation technique for discovering new periodic orbits in nonlinear dynamical lattices.
• To identify discrete breathers, which are localized, time-periodic solutions in these lattices.

Main Methods:

• Extension of the deflation numerical technique.
• Application to nonlinear dynamical lattices.
• Comparison of deflation approaches using Fourier decomposition and energy density profiles.

Main Results:

• Successfully identified discrete breathers in nonlinear dynamical lattices.
• Demonstrated the ability to find a wide variety of multibreather solutions.
• Showcased the method's effectiveness without prior knowledge of spatial profiles.

Conclusions:

• The extended deflation method is effective for discovering novel periodic orbits, specifically discrete breathers.
• The technique offers a robust way to explore complex solution branches in dynamical lattices.
• This approach facilitates the characterization of diverse multibreather solutions.