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Solitary wave formation under the interplay between spatial inhomogeneity and nonlocality
Konstantinos Dragonas1, Yannis Kominis1
1School of Applied Mathematical and Physical Science, National Technical University of Athens, Zographou GR-15773, Greece.
This study explores how spatial inhomogeneity and nonlocal nonlinearity affect solitary waves (SW). Researchers found these opposing forces can create diverse SW types, promising advanced applications.
Area of Science:
- Nonlinear physics
- Soliton theory
- Wave phenomena
Background:
- Spatial inhomogeneity restricts solitary wave (SW) formation to discrete locations.
- Nonlocal nonlinearity smooths medium response through averaging.
Purpose of the Study:
- Investigate the interplay between spatial inhomogeneity and nonlocal nonlinearity on SW formation and propagation.
- Determine conditions for different SW families (bright, kink).
Main Methods:
- Phase-space analysis for formation dynamics.
- Melnikov's method for analytical conditions.
- Numerical simulations for propagation dynamics.
Main Results:
- Analytical conditions derived for discrete bright SW and continuous kink SW families.
- Numerical evidence of stable, oscillatory, and transforming SW propagation.
- Demonstrated coexistence of different SW types under specific parameter relations.
Conclusions:
- The interplay of inhomogeneity and nonlocality enables diverse solitary wave behaviors.
- Tunable SW properties suggest potential for advanced applications in nonlinear systems.
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