Generalized lax pair operator method and nonautonomous solitons

Abstract

The generalized Lax pair operator method and the concept of nonautonomous solitons in nonlinear and dispersive nonautonomous physical systems are introduced. Novel soliton solutions for the nonautonomous nonlinear Schrödinger equation (NLSE) models with linear and harmonic oscillator potentials 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 nonlinearity variations. The concept of the designable integrability of the variable coefficients nonautonomous NLSE is introduced. The nonautonomous soliton concept and the designable integrability can be applied to different physical systems, from hydrodynamics and plasma physics to nonlinear optics and matter-waves and offer many opportunities for further scientific studies