Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics

In nonlinear optics, the soliton transmission in different forms can be described with the use of nonlinear Schrödinger (NLS) equations. Here, the soliton transmission is investigated by solving the NLS equation with the reciprocal of the group velocity [Formula: see text] , the group velocity dispersion coefficient [Formula: see text] and nonlinear coefficient [Formula: see text]. Two-soliton solutions for the NLS equation are obtained through the Hirota method. According to the solutions obtained, [Formula: see text] and [Formula: see text] with different function forms are taken to study the characteristics of solitons. The effect of the phase shift on the soliton interaction is discussed, and the non-oscillating soliton amplification, which is transmitted in a bound state, is explored. Parabolic solitons with oscillations are analysed. Moreover, parabolic solitons can be reduced to dromion-like structures. Results indicate that the transmission of solitons can be adjusted with the group velocity dispersion and Kerr nonlinearity coefficients. The phase shift, amplification, oscillation and attenuation of solitons can also be controlled by other related parameters. This work accomplishes the theoretical study of transmission characteristics of optical solitons in spatially dependent inhomogeneous optical fibres. The conclusions of this research have theoretical guidance for the research of optical amplifier, all-optical switches and mode-locked lasers.