A family of effective equations that capture the long time dispersive effects of wave propagation in heterogeneous media in an arbitrary large periodic spatial domain Ω ⊂ Rd over long time is proposed and analyzed. For a wave equation with highly oscillatory periodic spatial tensors of characteristic length ε, we prove that the solution of any member of our family of effective equations are ε-c...

this paper describes the effects of induced magnetic field and partial slip on the peristaltic flow of a couple stress fluids in an asymmetric channel. the two dimensional equation of couple stress fluid are simplified by making the assumptions of long wave length and low reynolds number. the exact solutions of reduced momentum equation and magnetic force function have been computed in wave fra...

New manifestly gauge-invariant forms of two-dimensional generalized dispersive long wave and NizhnikVeselov-Novikov systems of integrable nonlinear equations are presented. It is shown how in different gauges from such forms famous two-dimensional generalization of dispersive long wave system of equations, Nizhnik-Veselov-Novikov and modified Nizhnik-Veselov-Novikov equations and other known an...

In this paper we implement the unified rational expansion methods, which leads to find exact rational formal polynomial solutions of nonlinear partial differential equations (NLPDEs), to the (1+1)dimensional dispersive long wave and Clannish Random Walker’s parabolic (CRWP) equations. By using this scheme, we get some solutions of the (1+1)-dimensional dispersive long wave and CRWP equations in...

The equal width wave (EW) equation is a model partial differential equation for the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes. The EW-Burgers equation models the propagation of nonlinear and dispersive waves with certain dissipative effects. In this work, we derive exact solitary wave solutions for the general form of the EW equation and the gen...

We study dispersive properties of one-dimensional surface waterwaves under surface tension, based on the formulation of the problem as a nonlinear dispersive equation coupled with a transport-type equation. We establish a dispersion estimate on time scales depending on the size of the frequencies. We infer that, if s is large enough, then a solution u of the dispersive equation satisfies local-...

We consider the linearization of the three-dimensional water waves equation with surface tension about a flat interface. Using oscillatory integral methods, we prove that solutions of this equation demonstrate dispersive decay at the somewhat surprising rate of t−5/6. This rate is due to competition between surface tension and gravitation at O(1) wave numbers and is connected to the fact that, ...

A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, eg. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissip...

We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave often referred to as the shock wave refraction. The dispersive shock wave (DSW) refraction due to its head-on collision with the centred rarefaction wave (RW) is considered in the frameworks of the one-dimensional defocusing nonlinear Schr...