Darboux transformations, solitons, breathers and rogue waves for the modified Hirota equation with variable coefficients in an inhomogeneous fiber

Abstract

Investigated in this paper is the modified Hirota equation with variable coefficients, which can describe the amplification or absorption of pulses propagating in an inhomogeneous optical fiber. We construct a couple of the Darboux transformations, and obtain the one-soliton, two-soliton, breather and rogue-wave solutions. Effects of the group velocity dispersion, third-order dispersion, nonlinear focus length and velocity of propagation are graphically analyzed. Bell-, parabolic-, cubic- and periodic-type solitons are obtained. Bound state and head-on interactions for the two solitons are presented, with those interactions shown to be elastic. We can see two types of the breathers there, including the Akhmediev breathers and Kuznetsov–Ma solitons, and the rogue-wave pair consisting of two rogue waves is obtained.