Bright-dark rogue wave transition in coupled ab system via the physics-informed neural networks method. (English) Zbl 07882862
Summary: Physics-informed neural networks (PINNs) can be used not only to predict the solutions of nonlinear partial differential equations, but also to discover the dynamic characteristics and phase transitions of rogue waves in nonlinear systems. Based on improved PINNs, we predict bright-dark one-soliton, two-soliton, two-soliton molecule and rogue wave solutions in a coupled AB system. We find that using only a small number of dynamic evolutionary rogue wave solutions as training data, we can find the phase transition boundary that can distinguish bright and dark rogue waves, and realize the mutual prediction between different rogue wave structures. The results show that the improved algorithm has high prediction accuracy, which provides a promising general technique for discovering and predicting new rogue structures in other parametric coupled systems.
MSC:
| 65N99 | Numerical methods for partial differential equations, boundary value problems |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 68T07 | Artificial neural networks and deep learning |
| 68Q32 | Computational learning theory |
| 35C08 | Soliton solutions |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
| 35R02 | PDEs on graphs and networks (ramified or polygonal spaces) |
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