Rogue and solitary waves in coupled phononic crystals

In this work we present an analytical and numerical study of rogue and solitary waves in a coupled onedimensional nonlinear lattice that involves both axial and rotational degrees of freedom. Using a multiple-scale analysis, we derive a system of coupled nonlinear Schrodinger-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.

Automated summary

This work presents a theoretical and numerical study of rogue and solitary waves in a one-dimensional nonlinear lattice that involves axial and rotational degrees of freedom. Analytical approximations derived from coupled nonlinear Schrodinger-type equations are found to agree with numerical simulations. The spontaneous formation of rogue-wave-like patterns in the lattice using Gaussian initialization data is also observed. The lattice demonstrates both energy isolation and exchange between axial and rotational degrees of freedom, suggesting its potential as an efficient energy isolation, transfer, and focusing medium.