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Stability analysis for extended models of gap solitary waves
1Institut fur Theoretische Physik, Universitat Regensburg, Germany.
Summary
This study analyzes instabilities in nonlinear partial differential equations (PDEs) relevant to physical systems. Researchers identified translational and oscillatory instabilities, calculating their growth rates for gap soliton models.
Area of Science:
- Nonlinear Dynamics
- Mathematical Physics
- Computational Science
Background:
- Focuses on coupled nonlinear partial differential equations (PDEs) with complex variables.
- Extends the Mills-Trullinger gap soliton model, relevant to physical systems with frequency gaps.
Purpose of the Study:
- To perform a numerical linear stability analysis of localized solutions.
- To identify and characterize instabilities in specific PDE systems.
Main Methods:
- Employs numerical linear stability analysis.
- Investigates stationary spatially localized solutions of coupled nonlinear PDEs.
Main Results:
- Identifies translational and oscillatory instabilities.
- Computes growth rates of identified instabilities as a function of solitary wave parameters.
Conclusions:
- Provides a detailed stability analysis for a class of nonlinear PDEs.
- Offers insights into the behavior of gap soliton models and their localized solutions.
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