PT-symmetric solitons and parameter discovery in self-defocusing saturable nonlinear Schrödinger equation via LrD-PINN.

We propose a physical information neural network with learning rate decay strategy (LrD-PINN) to predict the dynamics of symmetric, asymmetric, and antisymmetric solitons of the self-defocusing saturable nonlinear Schrödinger equation with the PT-symmetric potential and boost the predicted evolutionary distance by an order of magnitude. Taking symmetric solitons as an example, we explore the advantages of the learning rate decay strategy, analyze the anti-interference performance of the model, and optimize the network structure. In addition, the coefficients of the saturable nonlinearity strength and the modulation strength in the PT-symmetric potential are reconstructed from the dataset of symmetric soliton solutions. The application of more advanced machine learning techniques in the field of nonlinear optics can provide more powerful tools and richer ideas for the study of optical soliton dynamics.

Deep neural network for modeling soliton dynamics in the mode-locked laser.

Integrating the information of the first cycle of an optical pulse in a cavity into the input of a neural network, a bidirectional long short-term memory (Bi_LSTM) recurrent neural network (RNN) with an attention mechanism is proposed to predict the dynamics of a soliton from the detuning steady state to the stable mode-locked state. The training and testing are based on two typical nonlinear dynamics: the conventional soliton evolution from various saturation energies and soliton molecule evolution under different group velocity dispersion coefficients of optical fibers. In both cases, the root mean square error (RMSE) for 80% of the test samples is below 15%. In addition, the width of the conventional soliton pulse and the pulse interval of the soliton molecule predicted by the neural network are consistent with the experimental results. These results provide a new insight into the nonlinear dynamics modeling of the ultrafast fiber laser.

Symmetry breaking of solitons in the PT-symmetric nonlinear Schrödinger equation with the cubic-quintic competing saturable nonlinearity.

The symmetry breaking of solitons in the nonlinear Schrödinger equation with cubic-quintic competing nonlinearity and parity-time symmetric potential is studied. At first, a new asymmetric branch separates from the fundamental symmetric soliton at the first power critical point, and then, the asymmetric branch passes through the branch of the fundamental symmetric soliton and finally merges into the branch of the fundamental symmetric soliton at the second power critical point, while the power of the soliton increases. This leads to the symmetry breaking and double-loop bifurcation of fundamental symmetric solitons. From the power-propagation constant curves of solitons, symmetric fundamental and tripole solitons, asymmetric solitons can also exist. The stability of symmetric fundamental solitons, asymmetric solitons, and symmetric tripole solitons is discussed by the linear stability analysis and direct simulation. Results indicate that symmetric fundamental solitons and symmetric tripole solitons tend to be stable with the increase in the soliton power. Asymmetric solitons are unstable in both high and low power regions. Moreover, with the increase in saturable nonlinearity, the stability region of fundamental symmetric solitons and symmetric tripole solitons becomes wider.