In this study, the generalized (3+1)-dimensional Shallow Water-Like (SWL) equation, which is one of evolution equations, taken into consideration. With help equation discussed, modified Kudryashov method, traveling wave solutions are successfully obtained. these solutions, graphs solitary waves to be obtained by giving special values arbitrary parameters presented. At same time, effect change v...

Considering the importance of ever-increasing interest in exploring localized waves, we investigate a generalized (3+1)-dimensional Hirota-Satsuma-Ito equation describing unidirectional propagation shallow-water waves and perform Painlev\'e analysis to understand its integrability nature. We construct explicit form higher-order rogue wave solutions by adopting Hirota's bilinearization polynomia...

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...

Dispersion analysis of discrete solutions to the shallow water equations has been extensively used as a tool to de ne the relationships between frequency and wave number and to determine if an algorithm leads to a dual wave number response and near 2 x oscillations. In this paper, we explore the application of two-dimensional dispersion analysis to cluster based and Galerkin nite element-based ...

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...

The superposition formulas of multi-solutions to the (3+1)-dimensional generalized shallow water wave-like Equation (GSWWLE) are proposed. There arbitrary test functions in mixed solutions and interaction solutions, we sum any N terms. By freely selecting positive integer N, have obtained abundant for GSWWLE. First, introduced new between two multi-kink solitons, were through symbolic computati...

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

in this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. the traveling wave hypothesis yields complexiton solutions. subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. the constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

The homogeneous balance method can be used to construct exact traveling wave solutions of nonlinear partial differential equations. In this paper, this method is used to construct new soliton solutions of the (3+1) Jimbo--Miwa equation.

the homogeneous balance method can be used to construct exact traveling wave solutions of nonlinear partial differential equations. in this paper, this method is used to construct newsoliton solutions of the (3+1) jimbo--miwa equation.