Computational Soliton solutions for the variable coefficient nonlinear Schrodinger equation by collective variable method

The Collective Variable (CV) approach is introduced to explore a significant form of Schrodinger 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.

Automated summary

The Collective Variable (CV) approach is introduced to analyze a significant form of Schrodinger equation with variable coefficients and higher order effects. Numerical simulations using the Runge-Kutta method of order four are implemented to explore pulse parameters, showing fluctuations in pulse variables and periodicity in chirp, width, amplitude, phase, and frequency of soliton. Different values of pulse parameters demonstrate variations in collective variables of solitons.