A new nonlinear Schrödinger equation is derived, which describes a cluster of bosons interacting via the strongest force. Its numerical solution points that the cluster is stable only if the number of particles is exactly 131. The relevant kinetic and potential energies of the particles are also calculated and interrelated via the virial theorem. The developed concept is applied to electrostatic forces as well. The paper is dedicated to the centennial Anniversary of the wave-particle duality, proposed by Louis de Broglie in 1924.