Periodic transmission theory of circularly symmetric multi-ring solitons in nonlinear Schrödinger equation

Abstract

In this paper, the evolution characteristics of periodic transmission of circularly symmetric multi-ring solitons in optical nonlocal materials based on nonlinear Schrödinger equation are investigated in detail. The transmission expression of circularly symmetric multi-ring solitons has been derived. It was found that the number and size of rings in these solitons can be controlled by initial parameters. The transmission of circularly symmetric multi-ring solitons is similar to that of high-order temporal solitons in nonlinear fibers, exhibiting periodic variations. When the input energy is a specific value, the statistical width of circularly symmetric multi-ring solitons remains constant during transmission, otherwise it exhibits periodic changes, which can be considered as generalized breathing solitons. The influence of various parameters on the transmission characteristics has been analyzed in detail, and some important transmission characteristics have been intuitively demonstrated through numerical simulation.