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Non-reciprocal solitons in an active elastic solid.

Mario Sandoval1, Luis Aparicio1

  • 1Department of Physics, Complex Systems, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City 09340, Mexico.

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|November 25, 2025
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Summary

Active metamaterials with nonlinear interactions generate non-reciprocal solitons, exhibiting unidirectional growth and accelerated motion. This research extends the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations to active systems, demonstrating new possibilities for wave control.

Keywords:
active elastic solidsactive matternon-reciprocal solitons

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Area of Science:

  • Condensed Matter Physics
  • Nonlinear Dynamics
  • Metamaterials

Background:

  • Non-reciprocity is a phenomenon observed across various physical systems, including active metamaterials modeled as spring-mass systems.
  • Previous work demonstrated that active forces in linearly interacting spring-mass systems can induce unidirectional signal propagation.

Purpose of the Study:

  • To investigate the generation of non-reciprocal solitons by introducing nonlinear interactions into active metamaterials.
  • To extend established nonlinear wave equations, such as KdV and mKdV, to incorporate active forces and non-reciprocity.
  • To analytically and numerically study the dynamics of these novel non-reciprocal solitons.

Main Methods:

  • Modeling active metamaterials as discrete spring-mass systems with nonlinear interactions.
  • Coarse-graining the discrete model to derive continuum equations, extending KdV and mKdV.
  • Analytical solutions of the derived non-reciprocal KdV and mKdV equations.
  • Numerical simulations to validate analytical findings and explore soliton interactions.

Main Results:

  • The addition of nonlinear interactions to active metamaterials generates non-reciprocal solitons with time-evolving amplitude and accelerated motion.
  • The study successfully extends the KdV and mKdV frameworks to describe active, non-reciprocal systems.
  • Analytical solutions show good agreement with numerical simulations, confirming the model's validity.
  • The dynamics of interacting non-reciprocal solitons were investigated under various conditions.

Conclusions:

  • Active forces can be effectively utilized to introduce non-reciprocity into metamaterial systems.
  • Non-reciprocal solitons represent a new class of wave solutions with unique dynamic properties.
  • The developed theoretical framework provides a foundation for understanding and designing active nonlinear systems with controlled wave propagation.