To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Backlund transformation of Riccati equation. Based on tan...To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Backlund transformation of Riccati equation. Based on tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamotc-Sivashinsky equation and the set of （2＋1）-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.展开更多
Harris hawks optimization(HHO)algorithm is an efficient method of solving function optimization problems.However,it is still confronted with some limitations in terms of low precision,low convergence speed and stagnat...Harris hawks optimization(HHO)algorithm is an efficient method of solving function optimization problems.However,it is still confronted with some limitations in terms of low precision,low convergence speed and stagnation to local optimum.To this end,an improved HHO(IHHO)algorithm based on good point set and nonlinear convergence formula is proposed.First,a good point set is used to initialize the positions of the population uniformly and randomly in the whole search area.Second,a nonlinear exponential convergence formula is designed to balance exploration stage and exploitation stage of IHHO algorithm,aiming to find all the areas containing the solutions more comprehensively and accurately.The proposed IHHO algorithm tests 17 functions and uses Wilcoxon test to verify the effectiveness.The results indicate that IHHO algorithm not only has faster convergence speed than other comparative algorithms,but also improves the accuracy of solution effectively and enhances its robustness under low dimensional and high dimensional conditions.展开更多
In this paper,a Boussinesq hierarchy in the bilinear form is proposed. A Backlund transformation for this hierarchy is presented and the nonlinear superposition formula is proved rigorously.
A new system is generated from a multi-linear form of a （2＋1）- dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its （1＋...A new system is generated from a multi-linear form of a （2＋1）- dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its （1＋1）- dimensional reduction gives an integrable equation which has been studied via reduction skills. Here, we give this （1＋1）-dimensional reduction a simple bilinear form, from which a Backlund transformation is derived and the corresponding nonlinear superposition formula is built.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.10461006)the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China(Grant No.NJZZ07031)+1 种基金the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.200408020103)the Natural Science Research Program of Inner Mongolia Normal University,China(Grant No.QN005023)
文摘To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Backlund transformation of Riccati equation. Based on tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamotc-Sivashinsky equation and the set of （2＋1）-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.
基金supported by the National Natural Science Foundation of China(61872126)。
文摘Harris hawks optimization(HHO)algorithm is an efficient method of solving function optimization problems.However,it is still confronted with some limitations in terms of low precision,low convergence speed and stagnation to local optimum.To this end,an improved HHO(IHHO)algorithm based on good point set and nonlinear convergence formula is proposed.First,a good point set is used to initialize the positions of the population uniformly and randomly in the whole search area.Second,a nonlinear exponential convergence formula is designed to balance exploration stage and exploitation stage of IHHO algorithm,aiming to find all the areas containing the solutions more comprehensively and accurately.The proposed IHHO algorithm tests 17 functions and uses Wilcoxon test to verify the effectiveness.The results indicate that IHHO algorithm not only has faster convergence speed than other comparative algorithms,but also improves the accuracy of solution effectively and enhances its robustness under low dimensional and high dimensional conditions.
文摘In this paper,a Boussinesq hierarchy in the bilinear form is proposed. A Backlund transformation for this hierarchy is presented and the nonlinear superposition formula is proved rigorously.
文摘A new system is generated from a multi-linear form of a （2＋1）- dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its （1＋1）- dimensional reduction gives an integrable equation which has been studied via reduction skills. Here, we give this （1＋1）-dimensional reduction a simple bilinear form, from which a Backlund transformation is derived and the corresponding nonlinear superposition formula is built.
