LAUSR

Abstract We reveal remarkable, but obviously only formal analogies and parallels between the soliton behavior in external gravitational-like potentials and the cosmic dark energy and antigravitation effects. The introduced generalized and exactly integrable higher-order nonlinear Schrodinger equation model for the wave function of a soliton in the attractive gravitational-like potential implies the existence of many fundamental nonlinear phenomena in completely different systems, independent of the physical origin of the nonlinearity and the higher-order linear and nonlinear dispersion. We show that the proposed model is governed by nontrivial Galilean-like invariance and, under the exact integrability conditions given by the Lax pair, demonstrates important formal nonlinear-optical analogies with enigmatic cosmic dark energy and antigravitation effects. Guided by interesting, but only formal analogy between the linear Doppler red shift and the nonlinear soliton self-frequency red shift effects, we reveal nontrivial features of the soliton propagation scenario in the attractive gravitation-like potential. Namely, the soliton attraction in the gravitation-like potential is changed to strong repulsion similar to the Newtonian particle dynamics in the repulsive antigravitational field. The wave-function red-shift effect (which is accumulated linearly with the propagation distance) is conserved under the transformation from attractive to repulsive scenarios in the ordinary space–time domain.