Two-dimensional toroidal breather solutions of the self-focusing nonlinear Schr?dinger equation

We introduce the ring-like toroidal breather solutions of the (2 + 1)-dimensional nonlinear Schrodinger (NLS) equation with Kerr nonlinearity. When the width of the toroidal pulse is much smaller than its radius, the (2 + 1)-dimensional NLS equation in cylindrical coordinates can be approximated by the standard (1 +1)-dimensional NLS equation. Based on this NLS equation, we obtain the first-order toroidal breather solutions, and study their dynamic characteristics. In particular, we discover and present for the first time the toroidal Peregrine soliton. This research can be extended to other high-dimensional nonlinear equations and provides a practical method for the study of other high-dimensional nonlinear localized wave structures.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

We introduce ring-like toroidal breather solutions of the (2 + 1)-dimensional nonlinear Schrodinger equation with Kerr nonlinearity. By approximating the (2 + 1)-dimensional NLS equation in cylindrical coordinates with the standard (1 + 1)-dimensional NLS equation, we obtain the first-order toroidal breather solutions and investigate their dynamic characteristics. Notably, we discover and present the toroidal Peregrine soliton for the first time. This research can be extended to studying other high-dimensional nonlinear equations and provides a practical method for analyzing other high-dimensional nonlinear localized wave structures.