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The study of soliton interactions is of significance for improving pulse qualities in nonlinear optics. In this paper, interaction between two solitons, which is governed by the Hirota equation, is considered. Via use of the Hirota method, an analytic soliton solution is obtained. Then a two-period vibration phenomenon is observed. Moreover, turning points of the coefficients of higher-order terms, which are related with sudden delaying or leading, are found and analyzed. With different coefficient constraints, soliton interactions are discussed by different frequency separation with the split-step Fourier method, and characteristics of soliton interactions are exhibited. Through turning points, we get a pair of solitons which tend to be bound solitons but not exactly. Furthermore, we control a pair of solitons to emit at different emission angles. The stability of the two-period vibration is analyzed. Results in this paper may be helpful for the applications of optical self-routing, waveguiding, and faster switching.

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Please cite this article as: Y.-Q. Li, W.-J. Liu, P. Wong, L.-G. Huang, N. Pan, Dromion structures in the (2 + 1)-dimensional nonlinear Schrödinger equation with a parity-time-symmetric potential, Appl. Math. Lett. (2015), http://dx. AbstractIn this paper, the (2+1)-dimensional variable-coefficient nonlinear Schrödinger equation with a paritytime-symmetric potential UP 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.

With the modified Hirota method, analytic soliton solutions for the generalized cubic complex Ginzburg-Landau equation with variable coefficients are derived for the first time. Based on the analytic solutions, soliton amplification is realized by choosing corresponding parameters properly. Besides, physical effects affecting the soliton amplification are discussed. Furthermore, stability analysis is presented. Results in this paper may be of value in further understanding the soliton amplification in fiber laser, and helpful for the generation of supercontinuum.

a b s t r a c tInteractions of dromion-like structures in the (1 + 1) dimension variable coefficient nonlinear Schrödinger 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.