Deep learning neural networks for the third-order nonlinear Schrödinger equation: bright solitons, breathers, and rogue waves

Zijian Zhou,Zhenya Yan

Table 1. Comparisons of α, β and their errors in the different training data-set via deep learning.

Case Solution α Error of α β Error of β 1 Exact bright soliton 1 0 0.5 0 2 Bright soliton without perturbation 1.000 04 3.85 × 10−5 0.050 08 7.48 × 10−5 3 Bright soliton with a 2% perturbation 0.999 67 3.31 × 10−4 0.050 29 2.89 × 10−4