Inelastic interactions, numerical breathers and chaotic wave fields for a focusing Kundu–Eckhaus equation in a nonlinear optical fiber

Abstract

Investigation is made on a focusing Kundu–Eckhaus equation in nonlinear/quantum optics and fluid mechanics, for describing the optical properties of the femtosecond lasers and femtochemistry objects, and for examining the stability of the Stokes waves in weakly nonlinear dispersive media. We derive the one and two optical breather solutions via the Darboux transformation. Inelastic interactions between two single-hump optical breathers and between a single-hump optical breather and a double-hump optical breather are depicted. Numerical optical breathers are obtained via the split-step Fourier method: β affects the speeds of the numerical optical breathers and space energy distribution, while β has no effects on the total energy, where β is a real constant representing the quintic nonlinearity. Optical chaotic wave fields via three initial conditions, including the plane wave, one soliton and one breather, are derived. Among them, the optical chaotic wave field via the one breather is the most orderless via the probability density function. Total energy of the optical chaotic wave field via the one breather is the largest.