Emad H Zahran
Publications:
Bekir A., Shehata M., Zahran E.
Comparison Between the Exact Solutions of Three Distinct Shallow Water Equations Using the Painlevé Approach and Its Numerical Solutions
2020, Vol. 16, no. 3, pp. 463477
Abstract
In this article, we employ the Painlevé approach to realize the solitary wave solution to
three distinct important equations for the shallow water derived from the generalized Camassa –
Holm equation with periodic boundary conditions. The first one is the Camassa – Holm equation,
which is the main source for the shallow water waves without hydrostatic pressure that describes
the unidirectional propagation of waves at the free surface of shallow water under the influence
of gravity. While the second, the Novikov equation as a new integrable equation, possesses
a biHamiltonian structure and an infinite sequence of conserved quantities. Finally, the third
equation is the (3 + 1)dimensional Kadomtsev – Petviashvili (KP) equation. All the ansatz
methods with their modifications, whether they satisfy the balance rule or not, fail to construct
the exact and solitary solutions to the first two models. Furthermore, the numerical solutions
to these three equations have been constructed using the variational iteration method.
