New exact solutions for nonlinear fourth-order Ablowitz–Kaup–Newell–Segur water wave equation by the improved tanh(φ(ξ) 2 )-expansion method
Mehwish Rani, Naveed Ahmed, Sever S Dragomir
Abstract
In this paper, abundant exact wave solutions of fourth-order Ablowitz–Kaup–Newell–Segur water wave (AKNS) equation have been investigated by using the innovative and efficient method called improved [Formula: see text]-expansion method (IThEM). The obtained solutions for AKNS equation are in the form of hyperbolic, trigonometric, exponential, logarithmic functions that are completely new and distant from previously derived solutions. To have the knowledge of dynamical physical characteristics of this equation, some important solutions have been discussed graphically in the form of two and three-dimensional along with contour plots by selecting suitable parameters with the aid of Maple program. The achieved outcomes exhibit that this new method is efficient, direct, and provides different classes of families. This technique can solve many nonlinear differential equations having importance in different field of sciences.