Dark-soliton solutions for a variable-coefficient Kundu–Eckhaus equation in inhomogeneous optical fibers

Abstract

To account for the inhomogeneity of optical fiber media, we investigate a variable-coefficient Kundu–Eckhaus equation for optical pulse propagation. Under the integrable coefficient constraints, dark one-, two-, and three-soliton solutions are derived by means of gauge transformation and Hirota bilinear method. The results show that the variable coefficient r(x) mainly modulates the soliton trajectories, while both overtaking and head-on collisions of dark solitons remain elastic.

Inhomogeneous optical fibers are described by a variable-coefficient Kundu–Eckhaus equation. Via gauge transformation and Hirota bilinear method, we derive dark one-, two- and three-soliton solutions. The dispersion coefficient r(x) modulates soliton trajectories without altering intrinsic soliton profiles. Both overtaking and head-on collisions of dark solitons are elastic under integrable coefficient constraints