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Analytic two-dark soliton solutions for a variable–coefficient nonlinear Schrodinger equation are obtained via modified Hirota method. Parallel solitons are observed and soliton control such as the soliton compression is realized with different group velocity dispersion profiles. Besides, soliton interactions are investigated with the interaction distance being adjusted. In addition, soliton repulsive structures as well as attractive ones are obtained with exponential dispersion profile. Results in our research may be useful for the soliton control in inhomogeneous optical fibers, which will be a benefit to the realistic optical communication systems.

In this paper, the ( 2 + 1 ) -dimensional variable-coefficient nonlinear Schrodinger equation with a parity-time-symmetric potential U P T ( r , φ ) is investigated. With the separation of variables, the solutions for that equation are obtained. Via the obtained solutions, some dromion structures are derived with corresponding parameters, and the influences of them (especial parity-time-symmetry) are analyzed and studied. Results show that the parity-time-symmetric potential plays an important role for obtaining dromion structures.

The study of the complex Ginzburg–Landau equation, which can describe the fiber laser system, is of significance for ultra-fast laser. In this paper, dromion-like structures for the complex Ginzburg–Landau equation are considered due to their abundant nonlinear dynamics. Via the modified Hirota method and simplified assumption, the analytic dromion-like solution is obtained. The partial asymmetry of structure is particularly discussed, which arises from asymmetry of nonlinear and dispersion terms. Furthermore, the stability of dromion-like structures is analyzed. Oscillation structure emerges to exhibit strong interference when the dispersion loss is perturbed. Through the appropriate modulation of modified exponent parameter, the oscillation structure is transformed into two dromion-like structures. It indicates that the dromion-like structure is unstable, and the coherence intensity is affected by the modified exponent parameter. Results in this paper may be useful in accounting for some nonlinear phenomena in fiber laser systems, and understanding the essential role of modified Hirota method.

Interactions of dromion-like structures in the ( 1 + 1 ) dimension variable coefficient nonlinear Schrodinger equation are studied for the first time. Analytic solutions for this equation are obtained, and physical parameters for this equation are assumed to be the Gaussian and hyperbolic functions, respectively. With a suitable choice of the parameters in the solutions, two and four dromion-like structures are presented, and interactions between them are discussed. Influences of corresponding parameters are analyzed. Results in this paper may have the applications in nonlinear optics and plasma physics.

Pulse interactions affect pulse qualities during the propagation. Interactions between butterfly-shaped pulses are investigated to improve pulse qualities in the inhomogeneous media. In order to describe the interactions between butterfly-shaped pulses, analytic two-soliton solutions are derived. Based on those solutions, influences of corresponding parameters on pulse interactions are discussed. Methods to control the pulse interactions are suggested.