The Maxwell class exact solutions to the Schr\"odinger equation and continuum mechanics models
Mathematical Physics
2026-03-27 v1 math.MP
Abstract
By applying the nonlinear Legendre transform to the continuity equation, this paper derives exact solutions to the Schr\"odinger equation and the equations of continuum mechanics. A generalized Maxwell distribution has been used as the momentum density function. Explicit expressions for the vector fields of time independent flows, density distributions, quantum and classical potentials have been found, and a detailed mathematical and physical analysis of the results obtained has been carried out.
Keywords
Cite
@article{arxiv.2603.25433,
title = {The Maxwell class exact solutions to the Schr\"odinger equation and continuum mechanics models},
author = {E. E. Perepelkin and B. I. Sadovnikov and N. G. Inozemtseva and A. S. Medvedev},
journal= {arXiv preprint arXiv:2603.25433},
year = {2026}
}
Comments
51 pages, 12 figures