In this Letter, we study (2 + 1)-dimensional Boussinesq equation and (3 + 1)-dimensional KP equation by using the new generalized transformation in Homogeneous Balance Method (HBM). As a result, many explicit exact solutions, which contain new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained.  2002 Elsevi...

In this study, we have applied the modified exp -expansion function method (MEFM) to obtain exact travelling wave solutions for (3+1) dimensional Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation and (3+1)-dimensional Jimbo-Miwa (JM) equation. Dark soliton solution, dark-bright hyperbolic solution trigonometric of KZK JM been found by using method. After that, scratched 2D 3D graphs all obtained i...

We consider a new partial differential equation, of a similar form to the Camassa-Holm shallow water wave equation, which was recently obtained by Degasperis and Procesi using the method of asymptotic integrability. We prove the exact integrability of the new equation by constructing its Lax pair, and we explain its connection with a negative flow in the Kaup-Kupershmidt hierarchy via a recipro...

Using a traveling wave reduction technique, we have shown that Maccari equation, (2?1)-dimensional nonlinear Schrödinger equation, medium equal width equation, (3?1)-dimensional modified KdV–Zakharov– Kuznetsev equation, (2?1)-dimensional long wave-short wave resonance interaction equation, perturbed nonlinear Schrödinger equation can be reduced to the same family of auxiliary elliptic-like equ...

A well balanced numerical scheme based on stationary waves for shallow water flows with arbitrary topography has been introduced by Thanh et al. [18]. The scheme was constructed so that it maintains equilibrium states and tests indicate that it is stable and fast. Applying the well-balanced scheme for the one-dimensional shallow water equations, we study the early shock waves propagation toward...

In this paper, we study basic properties of the diffusive wave approximation of the shallow water equations (DSW). This equation is a doubly non-linear diffusion equation arising in shallow water flow models. It has been used as a model to simulate water flow driven mainly by gravitational forces and dominated by shear stress, that is, under uniform and fully developed turbulent flow conditions...

Providing an illustration of sound propagation in the Hormoz Strait ,this paper is about acoustic wave propagation in shallow water for a harmonic point source with low frequency, less than 1000 and solution of a homogenous Helmholtz equation using parabolic equation. C++ programming is used to solve Helmholtz equation [9] and MATLAB software is used to illustrate figures and animate them [6], ...