Consideration is given to the influence of an underwater landslide on waves at the surface of a shallow body of fluid. The equations of motion which govern the evolution of the barycenter of the landslide mass include various dissipative effects due to bottom friction, internal energy dissipation, and viscous drag. The surface waves are studied in the Boussinesq scaling, with time-dependent bat...

The continuous spectrum and soliton solutions for the Boussinesq equation are investigated using the ∂̄-dressing method. Solitons demonstrate quite extraordinary behavior; they may decay or form a singularity in a finite time. Formation of singularity (collapse of solitons) for the Boussinesq equation was discovered several years ago. Systematic study of the solitonic sector is presented. © 2002...

Enlargement of Lie super algebra B(0, 1) was given firstly. Then nonlinear super integrable couplings of the super classical Boussinesq hierarchy based upon this enlarged matrix Lie super algebra were constructed secondly. And its super Hamiltonian structures were established by using super trace identity thirdly. As its reduction, special integrable couplings of classical Boussinesq hierarchy ...

Trial equation method is a powerful tool for obtaining exact solutions of nonlinear differential equations. In this paper, the improved Boussinesq is reduced to an ordinary differential equation under the travelling wave transformation. Trial equation method and the theory of complete discrimination system for polynomial are used to establish exact solutions of the improved Boussinesq equation.

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...

We study two coupled systems of nonlinear partial differential equations, namely, generalized Boussinesq-Burgers equations and 2 1 -dimensional Davey-Stewartson equations. The Lie symmetry method is utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the 2 1 dimensional Davey-Stewartson eq...

We present a new implementation of the geometric method Cullen & Purser (1984) for solving semi-geostrophic Eady slice equations which model large scale atmospheric flows and frontogenesis. The is Lagrangian discretisation, where PDE approximated by particle system. An important property discretisation that it energy conserving. restate in language semi-discrete optimal transport theory exploit...

In this paper, we consider the infinite time horizon LQR optimal control problem for linearized Boussinesq system. The goal is to justify approximation by penalization of free divergence condition in context. We establish convergence results controls, solutions and Riccati operators when parameter goes zero. These are obtained under two different assumptions. first one treats linearization arou...

[1] Based on a literature overview, this paper summarizes the impact and legacy of the contributions of Wilfried Brutsaert and Jean-Yves Parlange (Cornell University) with respect to the current state-of-the-art understanding in hydraulic groundwater theory. Forming the basis of many applications in catchment hydrology, ranging from drought flow analysis to surface water-groundwater interaction...