Traveling wave solutions of conformable Duffing model in shallow water waves

Abstract

The Duffing equation is a nonlinear second-order differential equation. The equation describes the motion of a damped oscillator with a more complicated potential than in simple harmonic motion; in physical terms, it models, for example, a spring pendulum whose spring stiffness does not exactly obey Hooke’s law. It is also an example of a dynamical system that exhibits chaotic behavior. Nonlinear equations, such as Duffing model, exhibit significant spectral energy transfer for finite amplitude waves in shallow areas above the flat seafloor. In this paper, a method is proposed to solve nonlinear conformable Duffing model. The solutions found are hyperbolic function solutions. These solutions are new solutions.