Modern Physics Letters B

For a nonlinear Schrödinger–Hirota equation with the spatio-temporal dispersion and Kerr law nonlinearity in nonlinear optics, we derive a Lax pair, a Darboux transformation and two families of the periodic-wave solutions via the Jacobian elliptic functions dn and cn. We construct the linearly-independent and non-periodic solutions of that Lax pair, and substitute those solutions into the Darboux transformation to get the rogue-periodic-wave solutions. When the third-order dispersion or group velocity dispersion (GVD) or inter-modal dispersion (IMD) increases, the maximum amplitude of the rogue-periodic wave remains unchanged. From the rogue-dn-periodic-wave solutions, when the GVD decreases, the minimum amplitude of the rogue-dn-periodic wave decreases. When the third-order dispersion decreases, the minimum amplitude of the rogue-dn-periodic wave rises. Decrease of the IMD causes the period of the rogue-dn-periodic wave to decrease. From the rogue-cn-periodic-wave solutions, when the GVD increases, the minimum amplitude of the rogue-cn-periodic wave decreases. Increase of the third-order dispersion or IMD leads to the decrease of the period.

In the last decade, many potent analytical methods have been utilized to find the approximate solution of nonlinear differential equations. Some of these methods are energy balance method (EBM), homotopy perturbation method (HPM), variational iteration method (VIM), amplitude frequency formulation (AFF), and max–min approach (MMA). Besides the methods mentioned above, the Akbari–Ganji method (AGM) is a highly efficient analytical method to solve a wide range of nonlinear equations, including heat transfer, mass transfer, and vibration problems. In this study, it was constructed the approximate analytic solution for movement of two mechanical oscillators by employing the AGM. In the derived analytical method, both oscillator motion equations and the sensitivity analysis of the frequency were included. The AGM was validated through comparison against Runge–Kutta fourth-order numerical method and an excellent agreement was achieved. Based on the results, the highest sensitivity of the oscillation frequency is related to the mass. As $\alpha$ and $\beta$ increase, the slope of the system velocity and acceleration will increase.

The solid solutions of ${\mathrm{\text{Ca}}}_x{\mathrm{\text{Ba}}}_{1-x}{\mathrm{\text{Ga}}}_2{\mathrm{\text{S}}}_4(x=0,0.1,\dots ,1)$ were synthesized by solid-phase reactions from powder components of CaS, BaS, and Ga₂S₃. The temperature-concentration dependences of the Gibbs free energy of formation of ${({\mathrm{\text{CaGa}}}_2{\mathrm{\text{S}}}_4)}_x{({\mathrm{\text{BaGa}}}_2{\mathrm{\text{S}}}_4)}_{1-x}$ solid solutions from ternary compounds and phase diagrams of the CaGa₂S₄–BaGa₂S₄ were determined by a calculation method. It was revealed that continuous solid solutions are formed in these systems. The spinodal decomposition of ${({\mathrm{\text{CaGa}}}_2{\mathrm{\text{S}}}_4)}_x{({\mathrm{\text{BaGa}}}_2{\mathrm{\text{S}}}_4)}_{1-x}$ solid solutions into two phases is predicted at ordinary temperatures.

In this paper, we discuss the interaction of the rational function, hyperbolic as well as exponential function for the (3+1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation with the aid of Hirota’s bilinear approach. We find several families of lump-type solutions. This method is a powerful and advantageous mathematical tool for establishing abundant lump solutions of nonlinear partial differential equations. In order to illustrate their dynamic properties, some figures are plotted with determined parameters.

This paper proposes a new density gradient continuous traffic flow model, and analyzes the linear stability of the model, as well as the bifurcation type of the model. Numerical simulation of the new model verifies the usability of the model. From the perspective of system stability, the bifurcation analysis method is used to analyze the nonlinear traffic phenomena on the expressway. The equilibrium solution of the model is discussed. On this basis, Hopf bifurcation, saddle bifurcation and Bogdanov–Takens bifurcation are obtained, and the existence conditions and fractional types of Hopf bifurcation and saddle bifurcation are obtained. The traffic flow characteristics of Hopf bifurcation and saddle node bifurcation are analyzed.

The possibilities of movement and electrochemical reduction of fibroin macroions in the presence of tricalcium phosphate ions in the form of a nanocoating during electrolysis have been studied. The manifestation of a non-Newtonian flow of a mixture of macroions and ions in a shear flow, the conditions for their electrochemical reduction in the form of a nanocoating with uniform morphology, and thickness on the electrode surface are revealed. It was found that the excess ions in the mixture and the uneven relief of the electrode surface contribute to the formation of a nanocoating with an inhomogeneous and uneven thickness.

In this study, we have taken into account the time-fractional Ostrovsky–Benjamin–Bona–Mahony equation, which is a synthesis of the time-fractional Ostrovsky equation and time-fractional Benjamin–Bona–Mahony equations and contains both mathematical and physical properties. Traveling wave solutions are produced by using the Ostrovsky–Benjamin–Bona–Mahony equation that physically sheds light on the incoming wave event on the ocean surface, using the sub-equation and Bernoulli sub-equation function methods. These solutions are presented in hyperbolic, trigonometric, singular and dark (topological) soliton types. With the help of special values given to the coefficients in the solitons obtained, it is associated with the solutions in the literature and it is observed that the solitons produced in this study are more general. Graphs representing the stationary wave at any given moment are presented. The advantages and disadvantages as well as the similarities and differences of the method are discussed in detail. Also, the behavior of the wave and its refraction according to the velocity variable, which is a physically important factor of the traveling wave solution, is analyzed and supported by simulation.

The $S$ phase (Al₂CuMg) is an important strengthening phase for the Al–Zn–Cu–Mg alloys, which are widely used in the aerospace and transportation industries. First-principles calculations based on the density functional theory were used to investigate the effects of doping V, Nb, Cd, Ag, Ge and Sb elements on the $S$ phase. The results demonstrate that Ag atom can spontaneously dope into the $S$ phase. Ge and Sb doping can improve the toughness and plasticity of the $S$ phase. And doping Ge, V or Nb can reduce the anisotropy of the Al₂CuMg phase. The hardness of the Nb, V, Cd and Ag doped structures become larger than that of the pristine structure. The results of orbital hybridization in the partial density of states (PDOS) and the distribution in electron density difference (EDD) confirmed that the effect of doping elements and Al atoms has the greatest impact on the performance of the system, and the strength of the covalent bond of the system affects the main aspects of brittleness. This study provides a better theoretical understanding of the doped $S$ phase, providing guidance for improved composition design and performance optimization of Al–Zn–Cu–Mg alloys.

The integration of quantum key distribution (QKD) devices with the existing optical fiber networks is of great significance in reducing the deployment costs and saving fiber resources. Wavelength division multiplexing (WDM) is expected to be a desirable approach to fulfill this ultimate task. In this paper, we analyze the dominant noises in WDM-based QKD system and optimize the key parameters based on a modified model with 200 GHz channel spacing. Then, an appropriate decoy-state method is adopted to estimate the system performance considering statistical fluctuations. Finally, a three-layer artificial neural network is used to train and predict the optimal mean photon numbers within different situations. Our work provides a useful method for the parameters optimization of WDM-QKD system and accelerates the practical development of QKD that coexists with the current backbone fiber infrastructure.

The trigonometric quintic B-spline scheme is used in this research paper to research Zakharov’s (ZK) nonlinear dimensional equation’s numerical solution. The ZK model’s solutions explain the relationship between the high-frequency Langmuir and the low-frequency ion-acoustic waves with many applications in optical fiber, coastal engineering, and fluid mechanics of electromagnetic waves, plasma physics, and signal processing. Three recent computational schemes (the expanded $exp(\varphi )$-expansion method, generalized Kudryashov method, and modified Khater method) have recently been used to investigate this model’s moving wave solution. Many innovative solutions have been established in this paper to determine the original and boundary conditions that allow numerous numerical schemes to be implemented. Here, the trigonometric quintic B-spline method is used to analyze the precision of the collected analytical solutions. To illustrate the precision of the numerical and computational solutions, distinct drawings are depicted.

Urban traffic control has become a big issue to help traffic management in recent years. With data explosion, Intelligent Transportation System (ITS) is developing rapidly. ITS is an advanced data-based method for traffic control, which requires timely and effective information supply. This research aims at providing real-time and accurate traffic flow data by intelligent prediction method. Applying multiple road traffic flow data of the Caltrans Performance Measurement System (PeMS) and separating the time series, the mechanism of spatial-temporal differences was taken into consideration. Based on the basic Long Short-Term Memory (LSTM) model, an improved LSTM model with Dropout and Bi-structure (Bi-LSTM) for traffic flow prediction was presented. In the prediction process, we applied three models including the improved Bi-LSTM model, Gated Recurrent Unit (GRU) model and Linear Regression in the experiment, and made a comparison from aspects of model structure complexity, operating efficiency and prediction accuracy. To validate the portability of the prediction model, the features of traffic flow from different datasets were further analyzed. The experimental results show that the improved Bi-LSTM model performs best in traffic flow prediction with comprehensive rationality, which reaches an accuracy of about 92% when considering temporal differences. Particularly, the specific factors of traffic situations and locations which is more applicable to be predicted by the improved Bi-LSTM model are summarized considering spatial differences. This research proposes an advanced and accurate model to provide real-time and short-term traffic flow prediction data, which is of great help to intelligent traffic control. Considering the mechanism between model and road traffic properties, the results suggest that it is more applicable in urban commercial area.

Traveling wave solution is one of the effective methods for solving nonlinear partial differential equations. D’Alembert solution is a special kind of traveling wave solution. There have been many studies about D’Alembert solution. In this paper, we will solve D’Alembert-type wave solutions for (2+1)-dimensional generalized Nizhnik–Novikov–Veselov equation. Based on the Hirota bilinear transformation and velocity resonance mechanism, the states of soliton molecules composed of two solitons, three solitons and four solitons are studied. It is concluded that D’Alembert-type wave is closely related to soliton molecules.