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Nonlocality-induced modulational instability in coupled Hartree equations
1Department of Mathematics, University of Kalyani, Kalyani 741235, India.
Chaos (Woodbury, N.Y.)
|June 9, 2026
Summary
We studied coupled nonlocal nonlinear Hartree equations, finding that external potentials and interactions can lead to unstable states. This instability drives pattern formation and collective excitations in Bose-Einstein condensates and optical systems.
Area of Science:
- Nonlinear dynamics
- Quantum physics
- Optics
Background:
- Coupled nonlocal nonlinear Hartree equations model Bose-Einstein condensates and nonlinear optical media.
- Understanding stability is crucial for predicting system behavior.
Purpose of the Study:
- Analyze the emergence of standing-wave states and modulational instability.
- Determine conditions for the instability of uniform states.
- Explore pattern formation in coupled nonlocal systems.
Main Methods:
- Analytical stability analysis using a Lens-type transformation.
- Calculation of the modulational instability gain spectrum.
- Numerical simulations of system dynamics.
Main Results:
- Identified conditions leading to modulational instability.
- Observed rich dynamical behavior including phase segregation and overlapping patterns.
- Demonstrated the role of external potentials in controlling configurations.
Conclusions:
- Nonlinear coupling and external potentials drive spontaneous structure formation.
- Instability leads to complex dynamics and collective excitation modes.
- Findings are relevant for Bose-Einstein condensates and nonlinear optics.
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