Effects of integrability criterion on nonlinear Schrödinger equations with mixed derivatives: insights from the Rangwala–Rao equation.

This study explores the impact of the integrability criterion on nonlinear Schrödinger (NLS ) equations with mixed derivatives, specifically focusing on the Rangwala–Rao ( R R ) equation formulated by A. Rangwala in 1990. The objective of this investigation is to enhance our understanding of the dispersion effect by examining novel soliton wave solutions and their interactions. By doing so, we aim to gain insights into the behavior of the slowly changing envelope of the electric field and pulse propagation in optical fibers. To achieve this, we employ recent computational approaches, including the Sardar Sub-equation and modified rational methods, to identify distinctive solitary wave solutions for the analyzed model. The significance of studying the Rangwala–Rao equation lies in its potential contribution to the development of more efficient optical fiber communication systems. The presented numerical solutions in this paper showcase the dynamic nature of optical fiber pulse propagation, thereby highlighting the originality of this work compared to existing scholarly contributions. [ABSTRACT FROM AUTHOR]