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Much attention has been given to constructing Lie and Lie superalgebra for integrable systems in soliton theory, which often have significant scientific applications. However, this has mostly been confined to (1+1)-dimensional integrable systems, and there has been very little work on (2+1)-dimensional integrable systems. In this article, we construct a class of generalised Lie superalgebra that differs from more common Lie superalgebra to generate a (2+1)-dimensional super modified Korteweg-de Vries (mKdV) hierarchy, via a generalised Tu scheme based on the Lax pair method where the Hamiltonian structure derives from a generalised supertrace identity. We also obtain some solutions of the (2+1)-dimensional mKdV equation using the G′/G2 method.

Based on the nonlinearization technique, a binary Bargmann symmetry constraint associated with a new discrete 3 × 3 matrix eigenvalue problem, which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals, is proposed. A new symplectic map of the Bargmann type is obtained through binary nonlinearization of the discrete eigenvalue problem and its adjoint one. The generating function of integrals of motion is obtained, by which the symplectic map is further proved to be completely integrable in the Liouville sense. c ⃝2015 All rights reserved.

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We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1)-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalizedDp-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value ofpis 5.

In this paper, the load time-series measured from 2016 to 2018 in Qingdao is investigated in order to make a prediction more accurately by using an artificial neural network model combined with some regular and irregular features. The results of spectral analysis show that several periodic variations in diurnal, semidiurnal and weekly frequencies are prominent, and considered as critical parts of predictior variables of the training and test sets in this forecasting model. However, a significant decline of load happens during the national statutory festivals in China, and is more obvious with the longer holidays, which should be taken into account as abnormal conditions. Moreover, both temperatuer and hummity filtered out by mutual information method are also added as two essential weather factors to improve the prediction accuracy, especially in the hot summer. Finally, the comparative results of five different experiments in term of mean absolute percent error show that the forecasting model combined with all periodic and non-periodic factors outperforms the others with one single or a few of factors. This multifactorial model, taking fully account of internal charateristics of load data and external important influences, is proved more suitable to predict the load trend in Qingdao. INDEX TERMS Short-term load forcasting, artificial neural network, periodic and non-periodic factors, mean absolute percent error.