Eur. Phys. J. Plus (2017) 132: 136
https://doi.org/10.1140/epjp/i2017-11430-0

Regular Article

Dynamics of solitons to the ill-posed Boussinesq equation

¹ Department of Applied Mathematics, King Saud University, P.O. Box 22452, 11495, Riyadh, Saudi Arabia
² Department of Applied Mathematics, Firat University Turkey, 23119, Elazig, Turkey
³ Department of Applied Mathematics, Federal University Dutse, Jigawa, Nigeria

^* e-mail: minc@firat.edu.tr

Received: 19 December 2016
Accepted: 1 March 2017
Published online: 22 March 2017

Abstract

In this paper, we analyze the dynamic behavior of the ill-posed Boussinesq equation (IPBE) that arises in nonlinear lattices and also in shallow water waves. Some solitary wave solutions are obtained by using the solitary wave ansatz method and the Bernoulli sub-Ode. By applying the technique of nonlinear self-adjoint, a quasi self-adjoint substitution for the IPBE is constructed. The classical symmetries of the equation are constructed. Then, we used along with the obtained nonlinear self-adjoint substitution to construct a set of new conservation laws (Cls).