Derivation and rogue waves of the fractional nonlinear Schrödinger equation for the Rossby waves.

The Cartesian coordinate system is not sufficient to study wave propagation on the coastline or in the sea where the terrain is extremely complicated, so it is necessary to study it in an unconventional coordinate system, fractals. In this paper, from the governing equations of fluid, the fractional nonlinear Schrödinger equation is derived to describe the evolution of Rossby waves in fractal by using multi-scale analysis and perturbation method. Based on the equation, the rogue-wave solution is obtained by the integral preserving transformation to explain some serious threats at sea.

On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions.

In this paper, the (2+1)-dimensional generalized fifth-order KdV equation and the extended (3+1)-dimensional Jimbo-Miwa equation were transformed into the Hirota bilinear forms with Hirota direct method. In this process, the Hirota bilinear operator played a significant role. Based on the Hirota bilinear forms, the single soliton solutions and the single periodic wave solutions of these two types of equations were obtained respectively. Meanwhile, the figures of the single soliton solutions and the single periodic wave solutions were plotted. Furthermore, the results shed light on that when the amplitude of water wave approaches 0, the single periodic wave solutions tend to the single soliton solutions. The conclusion has been generalized from (2+1)-dimensional equations to (3+1)-dimensional equations.

The New Simulation of Quasiperiodic Wave, Periodic Wave, and Soliton Solutions of the KdV-mKdV Equation via a Deep Learning Method.

How to solve the numerical solution of nonlinear partial differential equations efficiently and conveniently has always been a difficult and meaningful problem. In this paper, the data-driven quasiperiodic wave, periodic wave, and soliton solutions of the KdV-mKdV equation are simulated by the multilayer physics-informed neural networks (PINNs) and compared with the exact solution obtained by the generalized Jacobi elliptic function method. Firstly, the different types of solitary wave solutions are used as initial data to train the PINNs. At the same time, the different PINNs are applied to learn the same initial data by selecting the different numbers of initial points sampled, residual collocation points sampled, network layers, and neurons per hidden layer, respectively. The result shows that the PINNs well reconstruct the dynamical behaviors of the quasiperiodic wave, periodic wave, and soliton solutions for the KdV-mKdV equation, which gives a good way to simulate the solutions of nonlinear partial differential equations via one deep learning method.

The Short-Term Load Forecasting Using an Artificial Neural Network Approach with Periodic and Nonperiodic Factors: A Case Study of Tai'an, Shandong Province, China.

Accurate electricity load forecasting is an important prerequisite for stable electricity system operation. In this paper, it is found that daily and weekly variations are prominent by the power spectrum analysis of the historical loads collected hourly in Tai'an, Shandong Province, China. In addition, the influence of the extraneous variables is also very obvious. For example, the load dropped significantly for a long period of time during the Chinese Lunar Spring Festival. Therefore, an artificial neural network model is constructed with six periodic and three nonperiodic factors. The load from January 2016 to August 2018 was divided into two parts in the ratio of 9 : 1 as the training set and the test set, respectively. The experimental results indicate that the daily prediction model with selected factors can achieve higher forecasting accuracy.

The Short-Term Load Forecasting for Special Days Based on Bagged Regression Trees in Qingdao, China.

There are many factors that affect short-term load forecasting performance, such as weather and holidays. However, most of the existing load forecasting models lack more detailed considerations for some special days. In this paper, the applicability of the bagged regression trees (BRT) model combined with eight variables is investigated to forecast short-term load in Qingdao. The comparative experiments show that the accuracy and speed of forecasting have some improvements using the BRT than the artificial neural network (ANN). Then, an indicator variable is newly proposed to capture the abnormal information during special days, which include national statutory holidays, bridging days, and proximity days. The BRT model combined with this indicator variable is tested on the load series measured in 2018. Experiments demonstrate that the improved model generates more accurate predictive results than BRT model combined with previously variables on special days.