Solitary and Periodic Wave Solutions of Fractional Zoomeron Equation

Abstract

The Zoomeron equation plays a significant role in many fields of physics, especially in soliton theory, such as helping to reveal new distinctive properties in different physical phenomena such as fluid dynamics, laser physics, and nonlinear optics. By using the Riccati–Bernoulli sub-ODE approach and the Backlund transformation, we search for soliton solutions of the fractional Zoomeron nonlinear equation. A number of solutions have been put forth, such as kink, anti-kink, cuspon kink, lump-type kink solitons, single solitons, and others defined in terms of pseudo almost periodic functions. The (2 + 1)-dimensional fractional Zoomeron equation given in a form undergoes precise dynamics. We use the computational software, Matlab 19, to express these solutions graphically by changing the value of various parameters involved. A detailed analysis of their dynamics allows us to obtain completely better insights necessarily with the elementary physical phenomena controlled by the fractional Zoomeron equation.