Document Type : Research Paper
Authors
1
Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran.
2
Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran.
3
Department of Mathematics, University Of Okara, Okara, Pakistan.
4
Department of Physics and Engineering Mathematics, Higher Institute of Engineering,El Shorouk Academy-11837, Cairo, Egypt.
5
Computer Engineering, Biruni University, Istanbul, Turkey.
6
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
Abstract
The weakly nonlinear Schrodinger equation (NLSE) describes wave phenomena in media characterized by weakly nonlinear dispersion. Widely applicable across diverse fields such as plasma waves, water waves, fiber optics, and Bose-Einstein condensates, the NLSE serves as a versatile model. This study focuses on investigating various solutions for the weakly nonlocal NLSE with parabolic law nonlinearity. Utilizing the Nucci reduction method (NRM), exact solutions, including dark and bright solitons and other traveling wave solutions, are extracted. This method proves valuable for identifying nonlocal symmetries of differential equations, serving as an efficient
mathematical tool for nonlinear problem-solving in engineering and related domains. Furthermore, a first integral for the model is derived through the reduction method. These findings are crucial for understanding soliton wave propagation in weakly nonlocal media with parabolic law nonlinearity, providing insights into wave dynamics for the proposed model. Finally, density 2D and 3D plots are presented to visually depict the physical behavior of some obtained solutions within the governing model.
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