In this study, the integrability conditions on mixed derivative nonlinear Schrödinger equations are the focus of this work. A. Rangwala mathematically defined these effects and dubbed this form the Rangwala–Rao equation (${ℛ}{ℛ}$) in 1990. Using innovative soliton wave solutions and their interactions, we hope to better understand how dispersion affects the electric field and pulse propagation in optical fibers. Generalized Khater (GKhat.) provides unique solitary wave solutions to the ${ℛ}{ℛ}$ problem. The pulses’ dynamical behavior through optical fibers is seen in these numerical simulations. The originality of the paper’s conclusions may be seen by contrasting our findings with those of other researchers.

在这项研究中，混合导数非线性薛定谔方程的可积性条件是这项工作的重点。A. Rangwala 在数学上定义了这些效应，并将其命名为 Rangwala–Rao 方程（${ℛ}{ℛ}$) 于 1990 年使用创新的孤子波解决方案及其相互作用，我们希望更好地了解色散如何影响光纤中的电场和脉冲传播。Generalized Khater (GKhat.) 为${ℛ}{ℛ}$问题。在这些数值模拟中可以看到脉冲通过光纤的动态行为。通过将我们的发现与其他研究人员的发现进行对比，可以看出该论文结论的独创性。