  By method of moving frame, the relativistic integrable nonlinear model for
real, Majorana type spinor fields in 1+1 dimensions is introduced and gauge
equivalence of this model with Papanicolau spin model on one sheet hyperboloid
is established. In terms of the so called double numbers, the model is
represented also as hyperbolic complex relativistic model, in the form similar
to the massive Thirring model. By using Hirota bilinear method, one dissipaton
solution of this model is constructed. We calculated first integrals of motion
for this dissipaton and show that it represents relativistic particle with
highly nonlinear mass. Analyzing resonance conditions for scattering of two
relativistic dissipatons, we find a solution describing resonant property of
the dissipatons.
