In this study, we consider the third order nonlinear Schrödinger equation (TONSE) that models the wave pulse transmission in a time period less than one-trillionth of a second. With the help of the extended modified method, we obtain numerous exact travelling wave solutions containing sets of generalized hyperbolic, trigonometric and rational solutions that are more general than classical ones. Secondly, we construct the transformation groups which left the equations invariant and vector fields with the Lie symmetry groups approach. With the help of these vector fields, we obtain the symmetry reductions and exact solutions of the equation. The obtained group-invariant solutions are Jacobi elliptic function and exponential type. We discuss the dynamic behaviour and structure of the exact solutions for distinct solutions of arbitrary constants. Lastly, we obtain conservation laws of the considered equation by construing the complex equation as a system of two real partial differential equations (PDEs).

在这项研究中，我们考虑了三阶非线性Schrödinger方程（TONSE），该方程对小于1万亿分之一秒的时间段内的波脉冲传输进行建模。借助扩展的改进方法，我们获得了许多精确的行波解，其中包含比经典解更通用的广义双曲，三角和有理解集。其次，我们利用李对称组方法构造了使方程组不变和向量场不变的变换组。借助这些矢量场，我们获得了方程的对称约简和精确解。所获得的群不变解是雅可比椭圆函数和指数型。我们讨论了任意常数的不同解的精确解的动力学行为和结构。