Deep learning neural networks for the third-order nonlinear Schrödinger equation: bright solitons, breathers, and rogue waves
Zijian Zhou,Zhenya Yan
Figure 6. Data-driven parameter discovery of μ and ν in the sense of bright soliton (7). (a) (b) display the learning result under bright soliton data set. (a1)–(a2) are calculated without perturbation. (b1)–(b2) are calculated with 2% perturbation. (a2) and (b2) exhibit absolute value of difference between real solution and the function represented by the neural network. The relative ${{\mathbb{L}}}^{2}-$norm error of q(x, t), u(x, t) and v(x, t), respectively, are (a1)–(a2) 8.0153 × 10−4, 1.0792 × 10−3, 1.2177 × 10−3, (b1)–(b2) 1.0770 × 10−3, 1.6541 × 10−3, 1.3370 × 10−3.