Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrödinger equation

• We consider a unified model for soliton management by an integrable integro-differential Schrödinger equation.
• Using Lax pair, the N-fold Darboux transformation for the equation is presented.
• The multi-soliton management is considered.
• The synchronized dispersive and nonlinear management is suggested.

We consider a wide class of integrable nonautonomous nonlinear integro-differential Schrödinger equation which contains the models for the soliton management in Bose–Einstein condensates, nonlinear optics, and inhomogeneous Heisenberg spin chain. With the help of the nonisospectral AKNS hierarchy, we obtain the N-fold Darboux transformation and the N-fold soliton-like solutions for the equation. The soliton management, especially the synchronized dispersive and nonlinear management in optical fibers is discussed. It is found that in the situation without external potential, the synchronized dispersive and nonlinear management can keep the integrability of the nonlinear Schrödinger equation; this suggests that in optical fibers, the synchronized dispersive and nonlinear management can control and maintain the propagation of a multi-soliton.