Variational method is important since it can reduce the order of the differential equation to make the equation simpler and obtain the optimal solution by the stationary condition. In this paper, we mainly study the complex nonlinear Fokas-Lenells equation (CNFLE), which is used to describe the propagation of short pulses in optical fibers. The traveling wave transformation is used to convert the CNFLE into the ODE, and the variational principle of the solution is obtained by the semi-inverse method. Based on the variational principle, the extended He 0 s variational method, which is based on the Ritz-like method, is employed to investigate the bright soliton, bright-like soliton, bright-dark soliton, and periodic wave solution. The absolute, real, and imaginary parts of the novel computational solutions are plotted through one example in the form of 3-D and 2-D contours. In addition, the physical explanation of the solutions is elaborated in detail. The results reveal that the variational method is straightforward, simple, and effective, which is expected to bring a light to the study of the traveling wave theory.

In order to improve the predicting performance of stock index movement, this study proposes a new predicting model called Twin Support Vector Machines (TWSVM), which will be used to predict the trend of Shanghai Securities Composite Index (SSCI) and Standard and Poor's 500 Index (S&P500 Index), respectively. Thirteen indicators constructed by stock index historical data are selected as input features of the predicting model. The predicting target is the stock index daily movement, up or down. The decision tree (DT), Naive‐Bayes (NB), random forests (RF), probabilistic neural network (PNN) and support vector machine (SVM) are set as contrast experiments. The experiment results indicate that the TWSVM predicting model has a better predicting performance on both stock price and index daily movement.

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