The solution of a wave equation in the Gauss-Mainardi-Codazzi formalism of
Weyl-Dirac theory is obtained in terms of the elliptic function. In particu
lar, by degenerating the elliptic function, plane-wave, wavepacket, kink an
d soliton results. Each particular solution corresponds to certain values o
f the curvature scaler and of the cosmological constant, so chat the entity
manifests different wave-particle properties in different geometric situat
ions. Associating a superconducting behaviour to matter, by means of the ki
nk solution, we find the dependences on the reduced temperature of the supe
rconducting parameters, in other words, we develop a thermodynamics of the
isolated particle. Using the soliton solution we show char for any particle
we can define a particular waveguide.