Non-reciprocal solitons in an active elastic solid.

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.