Periodic property of the time-fractional Kundu–Mukherjee–Naskar equation

Abstract

The Kundu–Mukherjee–Naskar equation (KMN) can model the data transmission in birefringent fibers through molecules or pulses in a few Femto-seconds. A fractional modification with Riemann-Liouville time-fractional derivative is suggested to take into account the discontinuous period, and the wave-train description is used to reduce the equation to a fractional nonlinear Schrödinger equation, which is further converted to a damping Duffing equation. Effective modification of the homotopy perturbation method is suggested to deal with the damping term.

Keywords

• Rogue waves
• Kundu–Mukherjee–Naskar equation
• Periodic solution
• Stability Analysis
• Normal form transformation
• Exp-function method