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Solitary waves in a nonintegrable chain with double-well potentials
1Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.
Physical Review. E
|October 24, 2019
Summary
Solitary waves in nonlinear spring lattices are stable and robust, unaffected by energy barriers. These waves can transmit information over long distances, even when interacting with other waves or boundaries.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Wave phenomena
Background:
- Investigates solitary waves in a 1D lattice with nonlinear springs exhibiting bistable behavior.
- The spring potential is nonconvex, featuring two stable phases separated by an unstable region.
Purpose of the Study:
- To analyze the properties and stability of solitary waves in this bistable system.
- To determine the key parameters governing solitary wave behavior and their potential for information transmission.
Main Methods:
- Analytical treatment with approximations.
- Extensive numerical simulations.
- Application of the Vakhitov-Kolokolov criterion for linear stability analysis.
Main Results:
- Solitary wave solutions are independent of the energy barrier between phases.
- Wave shape is determined by stiffness ratio and Maxwell's force to transition strain ratio.
- Solitary waves are stable above a critical velocity, practically stable over most velocities.
- Interactions with other waves or boundaries cause minor changes and trailing undulations.
Conclusions:
- Bistable nonlinear spring lattices are suitable for robust, long-distance information delivery.
- The system demonstrates resilience to interactions, preserving wave integrity.
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