Interactions of solitons, dromion-like structures and butterfly-shaped pulses for variable coefficient nonlinear Schrödinger equation

Investigation on interactions of various types of solitons plays an important role in the analysis of various physical mechanisms. In this paper, analytic two- and three-soliton solutions for the variable coefficient nonlinear Schrödinger (vcNLS) equation are obtained with the help of the Hirota method. Through choosing the related parameters of solutions, we present various types of soliton interactions, and analyze the influence of corresponding parameters on soliton interactions. Periodic and oscillatory interactions between parabolic solitons are observed firstly. The method to control the butterfly-shaped pulse interaction is provided. Those results have guiding effect on controlling the interaction of solitons in nonlinear optics and Bose-Einstein condensation.