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Composition relation between gap solitons and Bloch waves in nonlinear periodic systems.
1Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
Physical Review Letters
|April 28, 2009
Summary
Bloch waves in nonlinear periodic systems are infinite chains of fundamental gap solitons (FGSs). This reveals multiple FGS families within band gaps, enabling new multi-period wave solutions.
Area of Science:
- Nonlinear physics
- Condensed matter physics
- Wave phenomena
Background:
- Periodic systems exhibit complex wave behaviors like Bloch waves.
- Understanding the fundamental constituents of these waves is crucial.
- Nonlinearity introduces unique soliton solutions.
Purpose of the Study:
- To investigate the composition of Bloch waves in 1D nonlinear periodic systems.
- To establish a relationship between Bloch waves and fundamental gap solitons (FGSs).
- To predict and numerically verify the existence of multiple FGS families.
Main Methods:
- Numerical computation and mathematical analysis.
- Investigating Bloch waves at the center and edge of the Brillouin zone.
- Analyzing the structure of nonlinear periodic systems.
Main Results:
- Bloch waves are shown to be infinite chains of fundamental gap solitons (FGSs).
- A direct relationship between Bloch waves and FGSs is established.
- The existence of n families of FGSs in the nth band gap is predicted and numerically confirmed.
- A method to construct multi-period Bloch wave-like solutions is developed.
Conclusions:
- Bloch waves in 1D nonlinear periodic systems are fundamentally composed of FGSs.
- The number of FGS families in a band gap corresponds to the band gap order.
- This composition principle offers a novel approach to generating complex wave solutions.
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