Utilizing the modified Fourier neural operator to predict the dynamics of vector optical solitons

This paper introduces the study of operator learning into the research of the generalized coupled nonlinear Schrödinger equations, utilizing the modified Fourier neural operator (MFNO) to learn the nonlinear mapping from any functional parameter dependency to the solution, thereby obtaining a complete soliton solution space. The number of variable parameters in the soliton solutions used for training has been expanded from one to multiple. In terms of details, this paper studies the bright-bright one-soliton and two-soliton solutions in the Manakov model, the bright-dark one-soliton and two-soliton solutions in the mixed model, as well as rogue wave solutions and Akhmediev breather solutions in the generalized model. It also explores the MFNO's extreme learning capabilities. These theoretical findings provide valuable insights into optical fiber telecommunications and lay a foundation for enhancing modern communication systems by using temporal optical solitons as information carriers.