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Two-dimensional map for a curved Fermi-Pasta-Ulam chain.
1Department Of Physics, University Of Pune, Pune-411007, India.
Summary
Researchers derived a 2D map from a curved Fermi-Pasta-Ulam (FPU) chain, revealing stable discrete breather (DB) solutions. Numerical studies show regular orbits and commensurate states, linking homoclinic orbits to stationary DBs.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Mathematical physics
Background:
- The Fermi-Pasta-Ulam (FPU) chain is a fundamental model in nonlinear dynamics.
- Discrete breathers (DBs) are localized, time-periodic solutions in nonlinear lattices.
- Investigating DBs in curved FPU chains can reveal novel dynamical behaviors.
Purpose of the Study:
- To derive and analyze a two-dimensional map from a curved FPU chain model.
- To examine the stability of equilibrium points and the nature of trajectories in the map.
- To understand the relationship between the map's dynamics and the lattice's discrete breather solutions.
Main Methods:
- Derivation of a two-dimensional discrete map from the curved FPU chain model.
- Analytical examination of the stability of equilibrium points in the map.
- Numerical investigation of phase space trajectories for varying curvature strengths.
Main Results:
- The derived map supports exact discrete breather (DB) solutions with frequencies outside the phonon band.
- Stability analysis reveals the nature of equilibrium points.
- Numerical simulations show regular orbits and commensurate states in the phase space.
- Homoclinic map orbits are identified and attributed to stationary DB solutions.
Conclusions:
- The two-dimensional map effectively models the dynamics of the curved FPU chain concerning DBs.
- The stability and trajectory analysis provide insights into the system's complex behavior.
- The connection between homoclinic orbits and stationary DBs highlights a significant dynamical feature.
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