Closed form solutions for the generalized0fifth-order KDV equation by using the modified exp-function method

Abstract

• The new approach of modified exp-function method has been effectively executed. • Find exact soliton solutions to the non-linear partial differential equation. • We have applied successfully modified exponential function method to the generalized fifth- order KDV equation. We investigate solitary wave solutions of the generalized fifth-order Korteweg–de Vries equation, which includes additional terms such as cubic nonlinearity and fifth order linear dispersion, as well as two nonlinear dispersive terms, in addition to the traditional quadratic nonlinearity and third-order dispersion. The projected modified exponential function approach is used to find exact solitary wave solutions to this equation, and the dependence of their amplitude, width, and speed on the parameters of the governing equation is investigated. Depending on the equation parameters, the resultant solution can represent either an embedded or regular soliton. Hyperbolic, trigonometric, and rational function solutions are obtained as a result. The symbolic computation software Maple verifies the accuracy of all obtained solutions. Finally, 3D, 2D, and contour plots of some of the derived solutions are shown to demonstrate the model's physical look. Many scientific and oceanographic applications involving ocean gravity waves and other associated phenomena require our acquired conclusions in this work concerning our examined equation.