Complex systems (CS) are pervasive in many areas, namely financial markets; highway transportation; telecommunication networks; world and country economies; social networks; immunological systems; living organisms; computational systems; and electrical and mechanical structures. CS are often composed of a large number of interconnected and interacting entities exhibiting much richer global scal...

To study a nonlinear partial differential equation (PDE), the Painlev́e expansion developed by Weiss, Tabor and Carnevale (WTC) is one of the most powerful methods. In this paper, using any singular manifold, the expansion series in the usual Painlev́e analysis is shown to be resummable in some different ways. A simple nonstandard truncated expansion with a quite universal reduction function is u...

The Whitham-Broer-Kaup equation exists widely in shallow water waves, but unsmooth boundary seriously affects the properties of solitary waves and has certain deviations scientific research. aim this paper is to introduce its modification with fractal derivatives a space establish variational formulation by semi-inverse method. obtained principle shows conservation laws an energy form also hint...

and Applied Analysis 3 by considering a general fractional nonlinear nonhomogeneous partial differential equation with the initial condition of the following form: D α t U (x, t) = L (U (x, t)) + N (U (x, t)) + f (x, t) , α > 0, (13) subject to the initial condition D k 0 U (x, 0) = gk, (k = 0, . . . , n − 1) , D n 0 U (x, 0) = 0, n = [α] , (14) where D t denotes without loss of generality the ...

In this paper, we study explicit correspondences between the integrable Novikov and Sawada–Kotera hierarchies, and between the Degasperis–Procesi and Kaup–Kupershmidt hierarchies. We show how a pair of Liouville transformations between the isospectral problems of the Novikov and Sawada–Kotera equations, and the isospectral problems of the Degasperis–Procesi and Kaup–Kupershmidt equations relate...