Exploration of new solitons and phase characterization for the extended Gerdjikov–Ivanov equation

Abstract

In a dense wavelength division multiplexed (DWDM) system, extended Gerdjikov–Ivanov (GI) equation has been explored for kerr law nonlinearity using two different techniques. The employed techniques are effective for identifying exact results including their dynamic characteristics. To explore exact solutions of the governing equation unified method has been applied which is one of the best analytical techniques. These analytical solutions are in form of polynomial as well as rational function. By assigning the specific values to the parameters, dark and bright soliton has been extracted. Afterwards, for phase characterization, the equation has been studied using bifurcation. The system has been first turned into a planer dynamical system, and subsequently into a Hamiltonian system. Then the equilibrium points has been derived. The different phase portrait is plotted by simply giving parameters various values.

Keywords

• Gerdjikov–Ivanov model
• DWDM system
• Kerr law
• Unified method
• Soliton
• Qualitative analysis