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

Zijian Zhou,Zhenya Yan

Table 2. Comparisons of μ, ν and their errors in the different training data-set via deep learning.

Case Solution μ Error of μ ν Error of ν 1 Exact bright soliton 1 0 1 0 2 Bright soliton without perturbation 1.003 70 3.69 × 10−3 6.031 43 3.14 × 10−2 3 Bright soliton with a 2% perturbation 0.981 59 1.84 × 10−2 5.887 33 1.13 × 10−1