The general form of the cubic Boussinesq-type equation is considered. In special cases, this reduced to three different versions Boussinesq equations and also generalized modified equation. Using slowly varying envelope approximation perturbation reduction method transformed coupled nonlinear Schrodinger two-component solitary wave solution obtained. Explicit analytical expressions for shape pa...

submerged breakwaters are one of the shore protective structures. any discontinuity in these breakwaters causes changes on current parameters including speed and water surface profile. in this paper, discontinuous submerged breakwaters were modelled to investigate the changes in the wave and flow pattern.to investigate the phenomenon, three models including a shore with constant slope, a shore ...

In the last two decades there has been considerable research on model water wave equations and the stability of their solitary waves. Among them, the Boussinesq type models such as [2], [3] and [4] describe small amplitude long waves in water of finite length. In this paper we will study the one-dimensional Benney-Luke equation. Our goal is twofold we aim to illustrate the usefulness of the abs...

In this paper we study, from a numerical point of view, some aspects of stability of solitary-wave solutions of the Bona–Smith systems of equations. These systems are a family of Boussinesq-type equations and were originally proposed for modelling the two-way propagation of one-dimensional long waves of small amplitude in an open channel of water of constant depth. We study numerically the beha...

Submerged breakwaters are one of the shore protective structures. Any discontinuity in these breakwaters causes changes on current parameters including speed and water surface profile. In this paper, discontinuous submerged breakwaters were modelled to investigate the changes in the wave and flow pattern.To investigate the phenomenon, three models including a shore with constant slope, a shore ...

We rigorously establish that, in the long-wave regime characterized by the assumptions of long wavelength and small amplitude, bidirectional solutions of the improved Boussinesq equation tend to associated solutions of two uncoupled Camassa-Holm equations. We give a precise estimate for approximation errors in terms of two small positive parameters measuring the effects of nonlinearity and disp...

We establish global existence and uniqueness theorems for the two-dimensional non-diffusive Boussinesq system with viscosity only in the horizontal direction, which arises in Ocean dynamics. This work improves the global well-posedness results established recently by R. Danchin and M. Paicu for the Boussinesq system with anisotropic viscosity and zero diffusion. Although we follow some of their...

ABSTRACT In this paper, we have been acquired the soliton solutions of the Variant Boussinesq equations. Primarily, we have used the enhanced (G'/G)-expansion method to find exact solutions of Variant Boussinesq equations. Then, we attain some exact solutions including soliton solutions, hyperbolic and trigonometric function solutions of this equation. MATHEMATICS SUBJECT CLASSIFICATION 35 K9...

The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated nu...

Dispersive effects induced by weak hydrostatic imbalance in the presence of topography and stratification are incorporated into a new model of barotropic (vertically integrated) mesoscale ocean dynamics. This barotropic model is obtained by first expanding the solutions of three dimensional Euler-Boussinesq equations in a regular perturbation expansion in terms of the several small dimensionles...