Nonautonomous solitons in the continuous wave background of the variable-coefficient higher-order nonlinear Schrödinger equation

We reduce the variable-coefficient higher-order nonlinear Schrödinger equation (VCHNLSE) into constant-coefficient (CC) one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical soliton solutions embedded in the continuous wave background for the VCHNLSE. Then the excitation in advance and sustainment of soliton arrays, and postponed disappearance and sustainment of the bright soliton embedded in the background are discussed in an exponential system.