University of Guilan Computational Sciences and Engineering 2783-2503 5 1 2025 04 01 Investigate new soliton type solutions to a nonlinear partial Schrödinger differential equations with the new auxiliary equation approach and its modification 139 150 9156 10.22124/cse.2025.31755.1122 EN Samira Heidari Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran Mostafa Eslami Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran Rohollah Yousefian Department of Mathematics, NO.c. Islamic Azad University, Noor, Iran Mohammad Esmael Samei Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran Journal Article 2025 09 22 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. https://cse.guilan.ac.ir/article_9156_670c5ccf264aa63031e84b43efc094fa.pdf