ABSTRACT
Solitons—self-localized robust and long-lived nonlinear solitary waves that do not disperse and preserve their identity during propagation and after a collision—arise in any physical system possessing both nonlinearity and dispersion, diffraction or diffusion. Nonautonomous physical systems subjected to some form of external input are of great interest because they are much more common and realistic, and they are not as idealized as canonical autonomous ones. This chapter suggests that the interested reader can directly enjoy the Dirac law of mathematical beauty applied to the nonautonomous soliton concept. Genuinely, the “roots” of nonautonomous solitons are deeplying in the so-called “hidden” symmetries of the famous quantum mechanical equations, and there exist many fruitful analogies with coherent and squeezed states of a quantum mechanical harmonic oscillator. The chapter considers the most important “precursor” of the nonautonomous soliton concept to demonstrate further an important deep “connection in time”: the so-called coherent and squeezed states of the quantum mechanical linear harmonic oscillator.
