Rogue and solitary waves in coupled phononic crystals

TL;DR

This paper investigates rogue and solitary waves in a coupled nonlinear lattice with axial and rotational degrees of freedom, using analytical and numerical methods to understand their formation, dynamics, and energy transfer properties.

Contribution

It introduces a coupled nonlinear Schrödinger equation model for rogue and solitary waves in a coupled lattice, supported by analytical derivation and numerical validation.

Findings

Analytical and numerical results agree on wave behavior.

Gaussian initial data can spontaneously form rogue waves.

Energy exchange occurs between axial and rotational modes.

Abstract

In this work we present an analytical and numerical study of rogue and solitary waves in a coupled one-dimensional nonlinear lattice that involves both axial and rotational degrees of freedom. Using a multiple-scale analysis we derive a system of coupled nonlinear Schr\"odinger type equations in order to approximate solitary waves and rogue waves of the coupled lattice model. Numerical simulations are found to agree with the analytical approximations. We also consider generic initialization data in the form of a Gaussian profile and observe that they can result in the spontaneous formation of rogue wave-like patterns in the lattice. The solitary and rogue waves in the lattice demonstrate both energy isolation and exchange between the axial and rotational degrees of freedom of the system. This suggests that the studied coupled lattice has the potential to be an efficient energy isolation, transfer, and focusing medium.