By means of a particle model that includes interactions only via the local concentration, we show hyperballistic diffusion may result. This is done by findng exact solution corresponding non-linear equation, as well simulations. The connection between these levels description provided Fokker-Planck equation describing dynamics. PACS numbers:

This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the ( G′ G ) -expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic so...

This paper considers the non-linear Kudryashov's equation, that is an extension of well-known dual-power law refractive index and analog to generalized version anti-cubic non-linearity. The model considered in presence full main objective this extract soliton solutions proposed model. Three state-of-the-art integration schemes, namely modified auxiliary equation method, sine-Gordon expansion me...