Prediction of Self-Similar Waves in Tapered Graded Index Diffraction Decreasing Waveguide by the A-gPINN Method

In this paper, an adaptive gradient-enhanced physics-informed neural network method(A-gPINN) is proposed to investigate the dynamics of solitons in tapered refractive index waveguides. A-gPINN method adopts adaptive sampling and incorporates the gradient information of the nonlinear partial differential equation into the neural network. Compared to traditional methods, A-gPINN can achieve a more accurate prediction of complicated soliton structures in a larger computational domain with less training data. Using this method, the evolution of self-similar bright solitons, self-similar soliton pairs, self-similar rogue waves, and self-similar Akhmediev breathers has been successfully and accurately predicted, while the coefficient variations of the generalized non-homogeneous nonlinear Schrödinger equation have been predicted reversely. Due to the superiority of this method, it turns to be a promising neural network method for studying soliton dynamics in optical fibers, and it also has application potential in other physical fields such as nonlinear optics and Bose Einstein condensation.