Exact traveling wave solutions and soliton solutions of conformable M-fractional modified nonlinear Schrödinger model

Abstract

The traveling wave solutions and soliton solutions of the conformable M-fractional modified nonlinear Schrödinger equation have been devised in this work by employing the generalized projective Riccati equations technique. The proposed method is straightforward and concise to obtain exact soliton solutions of nonlinear partial differential equations in various scientific discipline. This approach has been applied successfully to a wide variety of physical and mathematical problems. In many cases, the method has been able to provide new insights into the behavior of these systems and has led to the discovery of new phenomena. Several types of soliton solutions, including hyperbolic traveling wave solution, kink-shape soliton solution, singular soliton solution and dark soliton-type traveling wave solution, have been derived from the governing equation by using this effective technique. The solutions achieved by the governing model contain significant and dynamic justifications for certain real-world physical phenomena. Some acquired soliton solutions are displayed in 3D plots, corresponding contour plots and density plots to illustrate the physical dynamics of the governing model. Furthermore, the resulting outcomes manifest that the proposed method is highly efficient for revealing wave solutions for a wide range of nonlinear partial differential equations that emerge in optics.