Search

Abstract: In this paper, by considering the modified Adomian decomposition method (mADM), exact and numerical solutions are calculated for the generalized Zakharov equation which is an imaginary equation, with initial condition. The method does not need linearization, weak nonlinearity assumptions or perturbation theory. We compare the numerical solutions with corresponding analytical solutions. [Copyright &y& Elsevier]

We construct the extended physics-informed neural network with dual subnets to study the coupled saturable nonlinear Schrödinger equation, and predict the dipole-dipole, tripole-dipole and dipole-tripole vector soliton solutions. From the comparison between prediction and numerical solutions, evolutionary process prediction and loss function, the extended physics-informed neural network can be used to solve the coupled saturable nonlinear Schrödinger equation, and continuously optimize the prediction of model parameters by improving learning rate and loss function. The errors of dipole-dipole, tripole-dipole and dipole-tripole vector soliton solutions increase along the transmission distance, and they are mainly concentrated in the middle part of soliton structures. Moreover, model parameters are predicted through three different types of input data, and predicted results are compared. These results have certain reference value for predicting the transmission process of optical solitons using the machine learning. • Extended PINN with dual subnets is used to predict multipole vector solitons. • The performance of PINNs is compared from viewpoints of the number of iterations, hidden layers, and neurons. • Model parameters are predicted and compared through three different types of input data. [ABSTRACT FROM AUTHOR]

This article explores the dynamic model of pure-quartic solitons (PQSs) in mode-locked fiber lasers. Firstly, the formation and dynamic behavior of the PQS attracted state in fiber lasers are investigated to demonstrate their exceptional stability, robustness, and predictability. Next, the transmission characteristics of single PQS in mode-locked fiber lasers is subsequently analyzed and compared to those of solitons generated while considering the effect of second-order dispersion. Finally, the evolution of multi-PQS molecules is explored, and a stability analysis method for these soliton molecules is proposed. The findings of this research are not only significant for a deeper understanding of nonlinear interaction mechanisms but also contribute to the development of ultrafast optical devices and offer new insights into the understanding and application of complex nonlinear systems. • Formation and dynamic behavior of PQS attracted state are firstly discovered and studied. • Analysis of the characteristics of single PQS in mode-locked fiber lasers. • A stability analysis method for multi-PQS molecules is proposed. [ABSTRACT FROM AUTHOR]

he modified physics-informed neural network method with the learning rate decay is used to study two types of non-integrable nonlinear Schrödinger equations with competing nonlinearities. Symmetric and asymmetric solitons of nonlinear Schrödinger equations with competing quadratic-cubic and cubic-quintic nonlinearities are respectively predicted. The predicted results are presented from multiple aspects such as evolution process, error and loss function, which shows that the modified physical information neural network can effectively predict dynamics of these symmetric and asymmetric solitons in two cases of competing nonlinearities. From the error graphs of numerical and predictive solutions, the error gradually increases and mainly concentrates on the peak parts as the transmission distance increases. By setting appropriate loss function and improving the learning rate, iteration times and other aspects, model parameters are predicted successfully, and the influence of different number of iterations, neurons and hidden layers on the prediction error is compared. These findings have the certain reference value for using machine learning to predict the dynamics of optical solitons for non-integrable models. [ABSTRACT FROM AUTHOR]

Three kinds of vector multipole solitons of fractional coupled saturable nonlinear Schrödinger equation are reported, including fractional dipole-dipole, dipole-tripole and tripole-dipole vector soliton solutions. Firstly, their existence domains, which are modulated by potential function parameters, are constructed in a certain interval. Secondly, the stable regions of three kinds of vector multipole solitons, which are modulated by the soliton power of each component, are found. The properties of solitons are explored through these existence and stability domains. Finally, the stability of three kinds of fractional vector multipole solitons is verified by the numerical evolution. Compared with the integer-order results, there are differences in the existence and stable regions of soliton solutions, and the Lévy index affects the existence and stability of vector multipole solitons. • Existence domains of fractional vector multipole solitons are given. • Stable regions of fractional vector multipole solitons are found. • Stability of fractional vector multipole solitons is verified by the numerical evolution. [ABSTRACT FROM AUTHOR]

A quasi-residual physics-informed neural network (QR_PINN) with efficient residual-like blocks, was investigated based on classical physics-informed neural network to solve nonlinear fractional Schrödinger equation and analyze the transmission of spatial optical solitons in saturable nonlinear media with fractional diffraction. A comprehensive verification of stable transmission of various solitons under PT-symmetric potential was carried out using the QR_PINN. In addition, the transmission of spatial optical solitons was studied under simple real potential (stable transmission) and complex Scarf-II potential (unstable transmission). The results show that the QR_PINN can accurately reconstruct the transmission of spatial optical solitons under fractional diffraction. Meanwhile, as the complexity of the potential function increases, the prediction accuracy of the QR_PINN slightly decreases. These results provide a new approach for the application of deep learning in the nonlinear fractional Schrödinger equation. [ABSTRACT FROM AUTHOR]

Vortex plays a certain stabilizing role for the ring in the coexistence state of ring dark and anti-dark solitons with vortex due to the interaction between solitons and vortex in Bose-Einstein condensation and nonlinear optics. The numerical results show that the Lévy index for the Fractional-order effect has a great influence on their propagation. When the Lévy index is the optimal value, the ring dark soliton can maintain stable transmission over a longer distance, and the ring anti-dark soliton can also maintain stable transmission over a certain distance. • The coexistence state of ring dark and anti-dark solitons with vortex is revealed. • Fractional-order effect on the stability of this coexistence state is studied. • The coexistence states in both Kerr nonlinear medium and saturable nonlinear medium are reported. [ABSTRACT FROM AUTHOR]