The concept of a quasi-particle and the non-probabilistic interpretation of wave mechanics

The “master” equation admits solitary-wave solutions/solitons that behave as quasi-particles (QPs). We stipulate that particles are our perception of the QPs (schaumkommen in Schrödinger's own words). We show the passage from the continuous Lagrangian of the field to the discrete Lagrangian of the centers of QPs and introduce the concept of (pseudo)mass. We interpret the membrane tension as an attractive (gravitational?) force acting between the QPs. Thus, a self-consistent unification of electrodynamics, wave mechanics, gravitation, and the wave-particle duality is achieved.