Data-driven multi-valley dark solitons of multi-component Manakov Model using Physics-Informed Neural Networks

In this paper, we employ a Deep Learning technique, namely Physics-Informed Neural Network for solving multi-component Manakov models. In particular, we consider three and four-coupled nonlinear Schrödinger equations. We show that in the former case, one of the components and two others can carry, respectively, a double valley dark soliton and asymmetric bright solitons. In the four-component Manakov model, all four components are predicted by PINN with high accuracy in which the first component is shown to be a triple-valley dark soliton. We compare the results with the exact solutions and bring out the ability of Deep Learning in solving coupled systems of nonlinear partial differential equations with high accuracy. The performance of the PINN in approximating the solutions is estimated by taking the squared difference between the exact and predicted squared magnitude of the solutions. We have also computed the L²-norm errors for real, imaginary and absolute-value components of the solutions to emphasize the accuracy of PINN.