Abstract
We show that the methodology based on the generalized inverse scattering transform (ST) provides a systematic way to discover the novel exactly integrable nonlinear Schroedinger equation modesl with varying dispersion, nonlinearity and gain or absorption. Novel soliton solutions for the nonautonomous nonlinear Schrodinger equation (NLSE) models with harmonic oscillator potential substantially extend the concept of classical solitons and generalize it to the plethora of nonautonomous solitons that interact elastically and generally move with varying amplitudes, speeds and spectra adapted both to the external potentials and to the dispersion and nonlinearilty variations. The nonautonomous soliton concept is a useful tool in optical solitons applications and opens novel possibilities for matter-wave solitons generation.
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