Optical solitons for the Lakshmanan-Porsezian-Daniel model by collective variable method

Abstract

The present study introduces a Collective Variable (CV) approach to investigate an important type of Schrödinger equation called the Lakshmanan-Porsezian-Daniel (LPD) model which has great deals in optical materials. A state of numerical simulation via the application of the fourth-order Runge-Kutta method is further employed for the numerical treatment of the resultant system of dynamical equations of motion. The CV method gives the dynamics of the pulse parameters. Graphical representations of the pulse width, amplitude, temporal position, chirp, frequency, and phase of the pulse verses the propagation coordinate are displayed, correspondingly. More so, a significant periodicity is observed in the soliton’s amplitude, width and chirp. Other vital features with regards to the present study are also deduced.

Keywords

• Optical soliton
• Lakshmanan–Porsezian–Daniel equation
• Nonlinear Schr¨odinger equation
• Collective variable method