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

Zijian Zhou,Zhenya Yan

Figure 5. Data-driven parameter discovery of α and β in the sense of bright soliton (7). (a1)–(a2) Bright soliton without perturbation. (b1)–(b2) Bright soliton with a 2% noise. (a2), (b2) The absolute value of difference between the modules of exact and learning bright solitons. The relative ${{\mathbb{L}}}^{2}-$norm errors of q(x, t), u(x, t) and v(x, t), respectively, are (a1)–(a2) 7.0371 × 10−4, 1.0894 × 10−3, 1.0335 × 10−3, (b1)–(b2) 9.4420 × 10−4, 1.4055 × 10−3, 1.2136 × 10−3.