Explicit mathematical construction of relativistic nonlinear de Broglie waves described by three-dimensional (wave and electromagnetic) solitons "piloted" (controlled) by corresponding solutions of associated linear Klein-Gordon and Schrödinger equations

Abstract

Starting from a nonlinear relativistic Klein-Gordon equation derived from the stochastic interpretation of quantum mechanics (proposed by Bohm-Vigier,(1) Nelson,(2) de Broglie,(3) Guerra et al.(4)), one can construct joint wave and particle, soliton-like solutions, which follow the average de Broglie-Bohm(5) real trajectories associated with linear solutions of the usual Schrödinger and Klein-Gordon equations. © 1991 Plenum Publishing Corporation.