Nonlinear wave mechanics

Nonlinear wave mechanics is constructed, based on Schrödinger-type equation with nonlinearity −bψ ln | ψ |2. This nonlinearity is selected by assuming the factorization of wavefunctions for composed systems. Its most attractive features are: existence of the lower energy bound and validity of Planck's relation E = h̵ω. In any number of dimensions, soliton-like solutions (gaussons) of our equation exist and move in slowly varying fields like classical particles. The Born interpretation of the wavefunction is consistent with logarithmic nonlinearity and we tentatively estimate the order of magnitude of the universal constant b.