On the soliton solutions to the Nizhnik-Novikov-Veselov and the Drinfel'd-Sokolov systems

Abstract

This study investigates the Nizhnik-Novikov-Veselov and the Drinfel'd-Sokolov systems by using the extended sinh-Gordon equation expansion method. The Nizhnik-Novikov-Veselov system is an isotropic Lax extension of the one-dimensional Kortewegde Vries equation and the Drinfel'd-Sokolov system is a nonlinear model that possesses some special forms of Lax pairs. Topological kink-type, topological, non-topological, compound topological-non-topological bell-type and singular soliton solutions are successfully constructed. Under the choice of suitable values of parameters, the 2D, 3D and contour graphs to some of the obtained solutions are plotted.