By using an extended ( ′ G )-expansion method, we construct the traveling wave solutions of the (2+1)dimensional Painleve integrable Burgers equations, the (2+1)-dimensional Nizhnik-Novikov-Veselov equations, the (2+1)-dimensional Boiti-Leon-Pempinelli equations and the (2+1)-dimensional dispersive long wave equations, where G satisfies the second order linear ordinary differential equation. By...

We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada–Kotera and Kaup–Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik–Veselov–Novikov system. We show how these forms imply both new and well-known two-dimensional integrable nonlinear equations: the Sawada–Kotera equation, Kaup–Kuperschmidt equation, disp...

This paper extends the (2+1)-dimensional Eckhaus-type dispersive long wave equations in continuous medium to their fractional partner, which is a model of non-linear waves fractal porous media. The derivation shown briefly using He?s derivative. Using semi-inverse method, variational principles are established for system, up now not discovered. obtained proved correct by minimizing functional w...

We consider in this paper the well-posedness for the Cauchy problem associated to two-dimensional dispersive systems of Boussinesq type which model weakly nonlinear long wave surface waves. We emphasize the case of the strongly dispersive ones with focus on the “KdV-KdV” system which possesses the strongest dispersive properties and which is a vector two-dimensional extension of the classical K...

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-...

Abstract: In this paper, new algorithms called the “Modified exp( ́Ω)-expansion function method” and “Improved Bernoulli sub-equation function method” have been proposed. The first algorithm is based on the exp( ́Ω(ξ))-expansion method; the latter is based on the Bernoulli sub-Ordinary Differential Equation method. The methods proposed have been expressed comprehensively in this manuscript. The a...

In this paper, 1-lump solution and 2-lump of a (2 + 1)-dimensional Sawada-Kotera-like equation are obtained by means the Hirota’s bilinear method long wave limit method. The propagation orbits, velocities collisions among waves analyzed. By setting parameter values, dynamic characteristics solutions shown in 3D density plots. These conclusions enrich dynamical theory higher-dimensional nonlinea...