Abstract:
In search of the exact solutions of nonlinear partial differential equations in solitons form has become most popular to understand the internal features of physical phenomena. In this paper, we discovered various type of solitons solutions for the conformable space-time nonlinear Schrödinger equation (CSTNLSE) with Kerr law nonlinearity. To seek such solutions, we applied two proposed methods which are Sardar-subequation method and new extended hyperbolic function method. In this way several types of solitons obtained for example bright, dark, periodic singular, combined dark-bright, singular, and combined singular solitons. Some of the acquired solutions are interpreted graphically. These solutions are specific, novel, correct and may be beneficial for edifying precise nonlinear physical phenomena in nonlinear dynamical schemes. It is revealed that the proposed methods offer a straightforward and mathematical tool for solving nonlinear conformable space-time nonlinear Schrödinger equation. These results support in attaining nonlinear optical fibers in the future.
