New soliton solutions of fractional Biswas–Milovic equation with Kerr, parabolic and cubic-quartic nonlinearities

Abstract

This paper presents new explicit solutions of hyperbolic and trigonometric functions, obtained from the conformable fractional Biswas–Milovic equation, characterizing the long distance optical communications with three types nonlinearities: Kerr law, parabolic law and cubic-quartic ones. The Sardar sub-equation method is used, which gives the results that are of significant potential in a nonlinear system, providing a clear physical interpretation of the model under study. The resulting solutions are novel for the fractional Biswas–Milovic equation with the help of the method used, a powerful instrument for exploring precise solitary wave solutions for various other nonlinear equations in a nonlinear medium.