The aim of this paper are in two fold: First, introduce a new simplified bilinear method based on a transformation method combined with the Hirota bilinear sense. Second, apply this new technique to study the time-space fractional Boussinesq equation. To the best of my knowledge, the proposed work present new N-soliton solutions of the fractional Boussinesq equation. These new exact solutions e...

In the present study, the nonlinear Boussinesq type equation describe the bi-directional propagation of small amplitude long capillary–gravity waves on the surface of shallow water. By using the extended auxiliary equation method, we obtained some new soliton like solutions for the two-dimensional fourth-order nonlinear Boussinesq equation with constant coefficient. These solutions include symm...

We establish local and global existence results for Boussinesq type equations on a circle, employing Fourier series and a fixed point argument. 0. Introduction and Main Results. In the present work, we want to consider the question of existence and uniqueness of solutions for Boussinesq type equations (0.1) utt − uxx + uxxxx + ∂ xf(u) = 0, x ∈ T, t ∈ R, where T is the unit circle and f(u) is a ...

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...

Several Miura type transformations for the Boussinesq equation are found and the corresponding integrable systems constructed.

We consider a modified Boussinesq type equation. The Painlevé test of the WTC method is performed for this equation and it shows that the equation has weak Painlevé property. Some exact solutions are constructed.

We study Halphen’s equation and provide solutions in terms of elliptic functions of the second kind. The connection between Halphen’s equation and algebro-geometric solutions of the Boussinesq hierarchy is discussed.

In this paper we study a fractional diffusion Boussinesq model which couples a Navier-Stokes type equation with fractional diffusion for the velocity and a transport equation for the temperature. We establish global well-posedness results with rough initial data.

Similarity transforms of the Boussinesq equation in a semi-in®nite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial di€erential equation to a boundary-value problem. Chen et al. [Trans Porous Media 1995;18:15±36] use a hodograph method to derive an integral equation formulation of the new di€erential equation which they sol...