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In the present study, we investigate the symmetry groups of Benney equations that are the system of nonlinear integro-differential equations. We first investigate the symmetry groups of the Benney equations by using the method. Then we obtain all reduced forms of the system of integro-differential equations with fewer variables based on symmetry groups; and(More)
We consider a class of complex networks with both delayed and nondelayed coupling. In particular, we consider the situation for both time delay-independent and time delay-dependent complex dynamical networks and obtain sufficient conditions for their asymptotic synchronization by using the Lyapunov-Krasovskii stability theorem and the linear matrix(More)
In this study we introduce the general theory of Lie group analysis of integro-differential equations. A generalized version of the direct methods of determination of symmetry group of the point transformations is presented for the equations with nonlocal structure. First, the symmetry group definition of point transformations for the integro-differential(More)
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