Yang, "Time-fractional generalized Boussinesq equation
for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions," Applied Matheamtics and Computation, vol.
As shown in Figure 1, based on the Boussinesq equation
and following the above-mentioned assumptions, the differential equation of diving unsteady motion can be expressed as
Bichromatic signal deformation was also investigated by employing Boussinesq equation
Following Ma's method, the lump solutions for more nonlinear evolution equations have been found, for instance, the dimensionally reduced p-gKP and p-gBKP , the (2+1)-dimensional Boussinesq equation
, the BKP equation , the (3+1)-dimensional Jambo-Miwa , and the KdV equation .
In recent years, exact homoclinic and heteroclinic solutions were proposed for some NEEs like nonlinear Schrodinger equation, Sine-Gordon equation, DaveyStewartson equation, Zakharov equation, and Boussinesq equation
2.4 Connecting wave models based on Boussinesq equation
. Since numerical models based on the Navier-Stokes equation are very costly, wave models are frequently used to give necessary information at the offshore boundary of the calculation.
we receives Boussinesq equation
[4, 7, 9] to determine the deflections u:
Abazari, "Biswas, Solitary wave solutions of coupled Boussinesq equation
," Complixity, vol.
Li, "CRE solvability, exact soliton-cnoidal wave interaction solutions, and nonlocal symmetry for the modified Boussinesq equation
," Advances in Mathematical Physics, vol.
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.sup.p] norms of solutions.
Explicit series solution of Boussinesq equation
by homotopy analysis method, Journal of American Science, 8(11): 448-452.
 developed a numerical model (FUNWAVE) based on the fully nonlinear Boussinesq equations
by extending the Boussinesq equation
originally suggested by Peregrine .