Schrödinger solitons in gravitational-like potentials with embedded barriers and wells: Possible applications for the optical soliton supercontinuum generation and the ocean coast line protection

Abstract

Inspirited by many remarkable but, obviously, only formal analogies appearing within the framework of the nonlinear Schrödinger equation model from nonlinear femtosecond optics, Bose–Einstein condensates and plasmas, to ocean extreme waves and hurricanes, we conclude that these important mathematical parallels offer novel possibilities to perform “optic hydrodynamics” experiments in the nonlinear fiber-optics systems. Specifically, we present the results of the wide-range computer experiments of the soliton dynamics in the external gravitational-like potentials with embedded barriers and wells. We show that the external gravitational-like potential adds significant new physics both to the nonlinear soliton tunneling through classically forbidden potential barriers and to the solitonic analog of the quantum-mechanical Ramsauer–Townsend effect. The main special feature of a soliton in the external gravitational-like potential lies in the fact that its velocity is no longer constant, but depends linearly on time. This soliton acceleration changes dramatically the wave-particle duality of a soliton giving rise, by virtue of the Galilean symmetry, the appearance of its own solitonic analog of the “accelerating de Broglie wavelength”. Guided by this constructive (but obviously only formal) analogy, we reveal the hidden role of the soliton self-interaction (binding) energy both for the soliton nonlinear tunneling and the solitonic nonlinear analog of the Ramsauer–Townsend effect in the effective gravitational-like external potentials with superimposed barriers and wells.