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Abstract: This paper presents a novel differential evolution (DE) algorithm to solve the identification problem for Chen and Lü systems. A collection of unknown system parameters of Chen and Lü systems is taken as a manipulated parameter vector, and will be optimally evolved to approximate the actual parameters by using the proposed DE algorithm. Basically, the DE algorithm comprises three main operators of mutation, crossover, and selection to achieve the evolution. In the meanwhile, a cost function defined for solving the identification problem of chaotic systems is also minimized. Two illustrative examples are given to show the validity of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, the generalized F-expansion method [Chen J, He HS, Yang KQ. Commun Theor Phys (Beijing, China) 2005;44:307] is improved and a further improved F-expansion method is proposed to seek more types of exact solutions of non-linear evolution equations. With the aid of symbolic computation, we choose the (3+1)-dimensional Kadomstev–Petviashvili equation to illustrate the validity and advantages of the proposed method. As a result, many new and more general solutions are obtained including single and combined non-degenerate Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions. This method can also be applied to other non-linear evolution equations in mathematical physics. [Copyright &y& Elsevier]