Oscillatory motion of dissipative solitons induced by delay-feedback in inhomogeneous Kerr resonators

Data-driven soliton solutions and model parameters of nonlinear wave models via the conservation-law constrained neural network method

“…It can be seen from Table 3 that in the prediction of the interaction of the two soliton, we found that the prediction result of 3 L are not much different from the classic PINN. For the prediction of soliton molecule, we found that the prediction result of 3 L is better than the classical result. At the same time, it is found that the loss of 1 L is smaller than the loss of 5 L , but the prediction result is not as good as that of 5 L .…”

“…The data set can be similar to the KdV One-soliton discussion through the pseudo-spectrum. We found that the neural network with four different combinations of conservation laws predicts soliton interaction and soliton molecule, and the combination of 3 L has the best prediction result. It can be seen from Table 3 that in the prediction of the interaction of the two soliton, we found that the prediction result of 3 L are not much different from the classic PINN.…”

“…We found that the neural network with four different combinations of conservation laws predicts soliton interaction and soliton molecule, and the combination of 3 L has the best prediction result. It can be seen from Table 3 that in the prediction of the interaction of the two soliton, we found that the prediction result of 3 L are not much different from the classic PINN. For the prediction of soliton molecule, we found that the prediction result of 3 L is better than the classical result.…”

“…L L L to predict soliton solutions of the mKdV equation, which are the same as that of NLSE in the section 3. Similar to the KdV equation, the result of the loss combination 3 L is the best in the prediction for solution of mKdV equation, and its loss form is…”

“…Soliton theory has been deeply studied and widely used in mechanics, physics, biology, hydrodynamics and other engineering fields [1][2][3], and the essence of soliton is a special wave-like solutions of nonlinear wave models, namely nonlinear partial differential equations (NPDEs) [4].…”