Solving forward and inverse problems of the nonlinear Schr?dinger equation with the generalized PT-symmetric Scarf-Ⅱ potential via PINN deep learning

• 作者: Jiaheng Li Biao Li
• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2021,（12）
• 所属期刊栏目: MATHEMATICAL PHYSICS
• 页码范围: 1-13
• 页数: 13页
• 语种: 英文

摘要

In this paper,based on physics-informed neural networks(PINNs),a good deep learning neural network framework that can be used to effectively solve the nonlinear evolution partial differential equations(PDEs)and other types of nonlinear physical models,we study the nonlinear Schr?dinger equation(NLSE)with the generalized PT-symmetric Scarf-Ⅱ potential,which is an important physical model in many fields of nonlinear physics.Firstly,we choose three different initial values and the same Dirichlet boundary conditions to solve the NLSE with the generalized PT-symmetric Scarf-Ⅱ potential via the PINN deep learning method,and the obtained results are compared with those derived by the traditional numerical methods.Then,we investigate the effects of two factors(optimization steps and activation functions)on the performance of the PINN deep learning method in the NLSE with the generalized PT-symmetric Scarf-Ⅱ potential.Ultimately,the data-driven coefficient discovery of the generalized PT-symmetric Scarf-Ⅱ potential or the dispersion and nonlinear items of the NLSE with the generalized PT-symmetric Scarf-Ⅱ potential can be approximately ascertained by using the PINN deep learning method.Our results may be meaningful for further investigation of the nonlinear Schr?dinger equation with the generalized PT-symmetric Scarf-Ⅱ potential in the deep learning.