was derived for wave field without energy dissipation under the assumption of inviscid and irrotational flow, and is not theoretically applicable to wave fields with energy dissipation, such as breaking waves and turbulent flow field around coastal structures.
we receives Boussinesq equation
[4, 7, 9] to determine the deflections u:
The strategy is to express the abstract Boussinesq equation
as an integral equation with operator coefficient, to treat in the nonlinearity as a small perturbation of the linear part of the equation, then use the contraction mapping theorem and utilize an estimate for solutions of the linearized version to obtain a priori estimates on E-valued [L.
Zhang, "New double periodic and multiple soliton solutions of the generalized (2 + 1)-dimensional Boussinesq equation
," Chaos, Solitons and Fractals, vol.
The obtained dispersive wave equation can be reduced to the Boussinesq equation
under following assumptions:
Explicit series solution of Boussinesq equation
by homotopy analysis method, Journal of American Science, 8(11): 448-452.
From the original Boussinesq equation
the famous Korteweg-de V ries (KdV) equation follows.
The main types of stress according to Boussinesq equation
are written as follows:
Classical and nonclassical symmetries of a generalized Boussinesq equation
In recent years, with the development of fractional system rapidly, the classical Boussinesq equation
evolves into the fractional Boussinesq equation
, which is suitable for studying the water propagation through heterogeneous porous media [21-24].
A higher-order Boussinesq equation
in locally nonlinear theory of one-dimensional nonlocal elasticity.
Consideration of transient stream1aquifer interaction with the non-linear Boussinesq equation
using HPM, Journal of King Saud University, Science, in press, DOI: 10.