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Breathers in a discrete nonlinear Schrödinger-type model: Exact stability results
Avijit Lahiri1, Subhendu Panda, Tarun K Roy
1Department of Physics, Vidyasagar Evening College, Kolkata 700 006, India.
Summary
This study analyzes the stability of monochromatic breathers in a discrete nonlinear Schrödinger model. It reveals conditions for breather instability and explores multisite solutions, including antiphase breathers.
Area of Science:
- Nonlinear dynamics
- Mathematical physics
- Condensed matter theory
Background:
- Extends prior research on breather stability.
- Focuses on piecewise smooth discrete nonlinear Schrödinger-type models.
Purpose of the Study:
- Conduct an exact linear stability analysis of one-site monochromatic breathers.
- Investigate multisite monochromatic breather solutions and their stability.
- Clarify the behavior of two-site breathers in a limiting case.
Main Methods:
- Exact linear stability analysis.
- Identification of stability borders and critical spatial decay rates.
- Analysis of multisite breather solutions, including two-site antiphase breathers.
Main Results:
- One-site breathers destabilize above a critical spatial decay rate (lambda(c)).
- Two-site antiphase breathers exhibit a band of extended and localized eigenmodes.
- Destabilization occurs via Krein collision of growth rates, leading to temporal growth.
Conclusions:
- The model admits stable and unstable monochromatic breather solutions.
- Two-site breathers can decouple into independent one-site breathers in a specific limit.
- The model provides a framework for exploring complex breather dynamics, including vortex-type solutions.
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