Dromion-like structures in the variable coefficient nonlinear Schrödinger equation

Dromion-like structures, which have generally been investigated in the (2+12+1) or higher dimension partial differential equations, are reported in the (1+11+1) dimension variable coefficient nonlinear Schrödinger equation for the first time. With Hirota’s method, the analytic solutions for this equation are obtained. The concept of soliton management is introduced when the variable group-velocity dispersion and Kerr nonlinearity functions are suggested. Results show that the single and two dromion-like structures can be derived, and the single dromion-like structures can evolve into two dromion-like structures via different choices of the variable group-velocity dispersion and Kerr nonlinearity functions. The results of this paper will be valuable to the study of the Bose–Einstein condensate and nonlinear optical systems.