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Based on conservation laws as one of the important integrable properties of nonlinear physical models, we design a modified physics-informed neural network method based on the conservation law constraint. From a global perspective, this method imposes physical constraints on the solution of nonlinear physical models by introducing the conservation law into the mean square error of the loss function to train the neural network. Using this method, we mainly study the standard nonlinear Schr\"odinger equation and predict various data-driven optical soliton solutions, including one-soliton, soliton molecules, two-soliton interaction, and rogue wave. In addition, based on various exact solutions, we use the modified physics-informed neural network method based on the conservation law constraint to predict the dispersion and nonlinear coefficients of the standard nonlinear Schr\"odinger equation. Compared with the traditional physics-informed neural network method, the modified method can significantly improve the calculation accuracy.

This study aimed to investigate the antidepressant effects of Puyu Capsules and its potential mechanism. The antidepressant activity of Puyu Capsules was evaluated by forced swimming test(FST) and tail suspension test(TST) after subchronic administration in mice. Next, the mice were subjected to a chronic unpredictable stress(CUS) protocol for a period of 28 d to induce depressive-like behaviors. Then, a sucrose preference test, open-field test and novelty-suppressed feeding test were performed to evaluate the antidepressant effect of Puyu Capsules. After the behavioral test, the adrenal index was calculated; the levels of serum corticosterone(CORT) and adrenocorticotropic hormone(ACTH) were detected by enzyme-linked immunosorbent assay(ELISA); the levels of glucocorticoid receptor(GR), protein expression of brain-derived neurotrophic factor(BDNF), and the ratio of phosphorylated cAMP response element binding protein(CREB) to total CREB were detected by Western blot to explore the antidepressant function and mechanism of Puyu Capsules. The results suggested that Puyu Capsules had significant antidepressant effects on both the depression model and CUS model. At the same time, the drug could prevent the change of adrenal index induced by CUS and reverse the abnormal activation of CORT and ACTH in the serum of depressed mice. Finally, Puyu Capsules could also reverse the lower expression of pCREB, BDNF and GR in the hippocampus of CUS mice. In conclusion, Puyu Capsules produced significant antidepressant effects, and the mechanism was closely related to hypothalamic pituitary adrenal(HPA) axis activity, GR and CREB-BDNF pathway expression.

In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg—Landau equation with initial condition by considering the modified Adomian decomposition method (mADM), which is an efficient method and does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions are also compared with their corresponding analytical solutions. It is shown that a very good approximation is achieved with the analytical solutions. Finally, the modulational instability is investigated and the corresponding condition is given.

In this paper, the cylindrical KP-Burgers equation with variable coefficient for two-temperature ions in unmagnified dusty plasma with dissipative effects and transverse perturbations in cylindrical geometry is derived by using the standard reductive perturbation technique. With the help of variable-coefficient generalized projected Ricatti equation expansion method, the cylindrical KP-Burgers equation is solved and shock wave solution is obtained. The effects of some important parameters to the shock wave solution are illustrated from the wave evolution figures. The effects caused by dissipation and transverse perturbations are also discussed.

By using the density functional theory with B3LYP/6-31G+(d) we compute the optimization, vibration frequencies, electron structures of gg conformation of oligochitosans, and study the average binding energies and the zero-point energy corrections using WB97XD method. We also analyze the thermodynamic properties of oligochitosans. Results show that the hydrogen-bond makes the oligochitosan become spiral; average binding energies tend to decrease and stability tends to improve with the increasing degree of polymerization (DP); the water degradation of oligochitosan is an exothermic reaction, so it is feasible to reduce the temperature to improve the degradation yield in experiment; in addition, the energy gap of oligochitosan quickly converges to 6.99 eV with the increase of DP; furthermore, the value of DP7 oligochitosan is in accordance with the convergence value. The HOMO and LUMO of oligochitosan show that chemical activity is mainly distributed in C2 amino, C6 hydroxyl groups, and both ends of oligochitosan chain. These results have instructive significance on the modeling, and can provide a theoritical basis for degradation process, chemical activity position, and size-dependence in physical chemical properties of oligochitosan.

With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous (3+1)-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction, nonlinearity, harmonic potential and gain or loss when two constraints are satisfied. These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction, nonlinearity and the gain/loss. Based on these analytical results, we investigate the dynamic behaviours in a periodic distributed amplification system.

With the help of Maple procedure, the Zakharov equation, which takes the quantum effect into account, is solved by means of extended tanh-function method and bifunction method. Several solitary wave solutions are obtained, including bright soliton, W-shaped soliton, M-shaped soliton and singular solutions.