investigate new soliton type solutions to a nonlinear partial schrödinger differential equations with the new auxiliary equation approach and its modification

The central and fundamental subject of present research is to investigate the effective method of the new auxiliary equation approach for generalized schrödinger's equation. finding solutions to this equation has always been of great importance due to its applications in quantum mechanics and light propagation in nonlinear optical fibers. the results show that the proposed approaches are quite effective and efficient in obtaining exact solutions for nonlinear partial differential equations. due to the complexity of these equations' calculations, wolfram mathematica software has been used to validate the results of the proposed techniques.