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

Zijian Zhou,Zhenya Yan

Figure 4. Learning rogue wave solution related to equation (10) of the Hirota equation (2). (a1)–(a3) The unperturbated case, (b1)–(b3) the 2% perturbated case. The relative ${{\mathbb{L}}}^{2}-$norm errors of q(x, t), u(x, t) and v(x, t), respectively, are (a1)–(a3) 6.7597 × 10−3, 8.8414 × 10−3, 1.6590 × 10−2, (b1)–(b3) 3.9537 × 10−3, 5.8719 × 10−3, 9.0493 × 10−3.