Bifurcation and exact traveling wave solutions to a conformable nonlinear Schrödinger equation using a generalized double auxiliary equation method

This paper deals with a nonlinear Schrödinger equation in the sense of conformable derivative. Bifurcations and phase portraits are first proposed by using bifurcation theory, which investigates the dynamical behavior of this equation. This bifurcation theory classifies the plausible solutions to infinite periodic wave solutions, periodic wave solutions, two kink (anti-kink) wave solutions, and two families of breaking wave solutions. A generalized double auxiliary equation approach that generates three families of exact exact traveling wave solutions is then proposed using the conformable operator under various parameter conditions. The 3D behavior of various solutions with absolute real and imaginary parts is displayed. The obtained results show that the proposed methodology is efficient and applicable to a broad class of conformable nonlinear partial differential equations in mathematical physics.