Envelope vector solitons in nonlinear flexible mechanical metamaterials

TL;DR

This paper investigates the existence and properties of envelope vector solitons in a one-dimensional chain of flexible mechanical metamaterials, combining analytical and numerical methods to reveal new nonlinear wave solutions.

Contribution

It introduces a novel model for flexible mechanical metamaterials and derives an effective nonlinear Schrödinger equation to describe vector solitons with bright, dark, and kink-like profiles.

Findings

Support for envelope vector solitons with bright or dark rotational components

Longitudinal displacement exhibits kink-like profiles due to nonlinear coupling

Enrichment of nonlinear wave solutions in flexible mechanical metamaterials

Abstract

In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model the system, we formulate discrete equations that describe the longitudinal and rotational displacements of each individual rigid unit mass using a lump element approach. By applying the multiple-scales method in the context of a semi-discrete approximation, we derive an effective nonlinear Schr\"odinger equation that characterizes the evolution of rotational and slowly varying envelope waves from the aforementioned discrete motion equations. We thus show that this flexible mechanical metamaterial chain supports envelope vector solitons where the rotational component has the form of either a bright or a dark soliton. In addition, due to nonlinear coupling, the longitudinal displacement displays kink-like profiles thus forming the 2-components vector soliton. These findings, which include specific vector envelope solutions, enrich our knowledge on the nonlinear wave solutions supported by flexible mechanical metamaterials and open new possibilities for the control of nonlinear waves and vibrations.