In this paper, we have obtained new analytical solutions of (3+1)-dimensional SWW equation with Kudryashov method. The study Shallow water wave plays an imperative role in theory. For calculation software Maple is used. by method are new.

In this work we study analytically and numerically the performance of the mean heave motion of an OWC coupled with the governing equation of the spreading ocean waves due to the wide variation in an open parabolic channel with constant depth. This paper considers that the ocean wave propagation is under the assumption of a shallow flow condition. In order to verify the effect of the waves in th...

We investigate a (2+1)-dimensional shallow water wave equation and describe its nonlinear dynamical behaviors in physics. Based on the N -soliton solutions, higher-order fissionable fusionable waves, or waves mixed with soliton molecular breather can be obtained by various constraints of special parameters. At same time, long limit method, interaction between lumps are acquired. Combined dynami...

Euler’s equations describe the dynamics of gravity waves on the surface of an ideal fluid with arbitrary depth. In this paper, we discuss the stability of periodic travelling wave solutions to the full set of nonlinear equations via a non-local formulation of the water wave problem, modified from that of Ablowitz, Fokas & Musslimani (J. Fluid Mech., vol. 562, 2006, p. 313), restricted to a one-...

The Lie-group formalism is applied to investigate the symmetries of the Dullin-Gottwald-Holm equation φt −αφxxt +2wφx +3φφx + γφxxx = α(2φxφxx +φφxxx), which describes the unidirectional propagation of two dimensional waves in shallow water over a flat bottom. We derived the infinitesimals that admit the classical symmetry group. The reduced ordinary differential equation is further studied and...

Three-dimensional solitary waves or lump solitons are known to be solutions to the Kadomtsev–Petviashvili I equation, which models small-amplitude shallow-water waves when the Bond number is greater than 1 3 . Recently, Pego and Quintero presented a proof of the existence of such waves for the Benney–Luke equation with surface tension. Here we establish an explicit connection between the lump s...

We apply a multiple–time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a secularity–free perturbation theory, we show that the well known N–soliton dynamics of the shallow water wave equation, in the particular case of α = 2β, can be reduced to the N–soliton solution that satisfies si...

In this paper we develop a higher-order nonlinear Schrodinger equation with variable coefficients to describe how a water wave packet will deform and eventually be destroyed as it propagates shoreward from deep to shallow water. It is well-known that in the framework of the usual nonlinear Schrodinger equation, a wave packet can only exist in deep water, more precisely when kh > 1.363 where k i...