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This study explores nonlinear dynamics in classical chains, defining solitons without continuum theory. It investigates soliton transmission and reflection in inhomogeneous systems, revealing boundary dynamics.

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Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Soliton theory

Background:

  • Topologically protected zero-energy modes exist in classical chains, localized at boundaries.
  • Linearized equations capture static features, but nonlinearity governs dynamic behavior.

Purpose of the Study:

  • Investigate quasiperiodic solutions of nonlinear equations of motion in 1D classical chains.
  • Define solitons for discrete systems without continuum approximation.
  • Analyze soliton dynamics in inhomogeneous chains with distinct parameter sets.

Main Methods:

  • Studied quasiperiodic solutions of nonlinear equations of motion.
  • Defined solitons via periodic trajectories in configuration space.
  • Connected two chains with different parameters to examine soliton transmission/reflection.

Main Results:

  • Quasiperiodic solutions were identified, enabling soliton definition in discrete systems.
  • Soliton dynamics were analyzed at the boundary between inhomogeneous chains.
  • Transmission and reflection phenomena of solitons were observed at the boundary.

Conclusions:

  • Nonlinear dynamics are crucial for understanding localized modes in classical chains.
  • A discrete approach to soliton definition is viable and demonstrated.
  • Inhomogeneous systems exhibit complex soliton interactions at boundaries.