Dynamical behavior and exact solution in invariant manifold for a septic derivative nonlinear Schrödinger equation

Abstract

In this paper, we consider a pulse dynamics in nonlinear optics (fiber-optic communications) in the presence of both self-steepening and septic nonlinear effects. Propagating profiles of the septic derivative nonlinear Schrödinger model which are isolated via coupled integrable invariants of motion, that admits exact solution, are investigated by a method of dynamical systems. By investigating the dynamical behavior and bifurcation of phase portraits of the traveling wave system, we obtain possible explicit exact parametric representations of solutions under different parameter conditions.