Nonautonomous solitons of the novel nonlinear Schrödinger equation: Self-compression, amplification, and the bound state decay in external potentials

The generalized nonautonomous nonlinear Schrödinger equation is introduced in the framework of the nonisospectral generalization of the Inverse Scattering Transform method with associated spectral parameter varying in accordance with the Riccati equation. Nonautonomous solitons of the introduced model conserve the soliton main feature to interact elastically both in the linear, parabolic, and cubic external potentials, and are controlled only if the varying dispersion and nonlinearity satisfy to the conditions of the exact integrability. Novel features of nonautonomous solitons arising due to the dependence between the soliton amplitudes and their velocities consist in the decay of the soliton bound states. •New nonautonomous nonlinear Schrödinger equation.•Spectral parameter is varied in accordance with the Riccati equation.•Solitons of our model interact elastically in the linear, parabolic, and cubic potentials.•Dependence between the soliton amplitudes and their velocities.•The decay of the soliton bound states.•The nonuniformly accelerated soliton motion.•The external potentials in the form of a polynomial series with time-varying coefficients.