Conservation laws and breather-to-soliton transition for a variable-coefficient modified Hirota equation in an inhomogeneous optical fiber

Abstract

Optical fibers are used in the communications, biological sensors and chemical sensors. We investigate a variable-coefficient modified Hirota equation for the amplification or absorption of pulses propagating in an inhomogeneous optical fiber. With respect to the complex envelope of the optical field, we construct the infinitely-many conservation laws based on the existing Lax pair. According to the existing Darboux transformation, we derive the three-soliton solutions, the higher-order breather solutions and breather-to-soliton transition condition. Amplitudes of the two solitons change after the interaction, while velocities of them are unchanged via asymptotic analysis. When P(z)=0, interactions among the three parabolic or wavy solitons, interaction between the two parabolic or wavy or crooked breathers, and interactions among the three parabolic and wavy breathers are presented, where P(z) is related to the nonlinear focus length. Velocities of three solitons or two crooked breathers with P(z)≠0 are different from those with P(z)=0. Based on the breather-to-soliton transition condition, when P(z)=0, parabolic or wavy multi-peak and M-shaped solitons are presented; when P(z)≠0, the crooked periodic wave and anti-dark soliton are shown.