Prediction of the number of solitons for initial value of Nonlinear Schrödinger equation based on the deep learning method

Abstract

The number of solitons emerged in the given initial value for the Nonlinear Schrödinger equation (NLS equation) is explored by the deep learning method. Conventional neural network (CNN) is used to build the framework of prediction. The training data set is constructed by the short time evolution image of initial values of NLS equation by Fourier spectrum method and labeling them by theoretical results automatically, in other word, Zaharov-Shabat transform for special initial values in form of Asech(x). The prediction ability is verified by different kinds of initial values, including Gaussian initial value and Asech(Ax) initial value. CNN learns the relationship between spatiotemporal data and the number of solitons for given initial values of NLS equation effectively. This method can be used to other integrable equations.