The Collective Variable (CV) approach is introduced to explore a significant form of Schrödinger equation with variable coefficients and higher order effects. The state of numerical simulation through the utilization of the Runge-Kutta method of order four is further implemented to the resulting ordinary differential equations for pulse parameters. This technique furnishes the fluctuation of pulse variables. Graphical interpretation for the temporal position, amplitude, width, chirp, phase and frequency of the pulse versus the propagation coordinate is shown. Moreover, we observe a compelling periodicity in the chirp, width, amplitude, phase and frequency of soliton. For distinct values of pulse parameters, the numerical behavior of solitons is also given to show variations in collective variables.

引入了集体变量 (CV) 方法来探索具有可变系数和高阶效应的薛定谔方程的重要形式。通过利用四阶 Runge-Kutta 方法的数值模拟状态进一步实现到脉冲参数的所得常微分方程。该技术提供脉冲变量的波动。显示了脉冲的时间位置、幅度、宽度、线性调频、相位和频率与传播坐标的图形解释。此外，我们观察到孤子的啁啾、宽度、幅度、相位和频率具有引人注目的周期性。对于脉冲参数的不同值，还给出了孤子的数值行为以显示集体变量的变化。