The class of so called fundamentally finite integrable Vekua CDE is defined
using the fixed point of the inversion and where one solution is equal to
the coefficient of the equation. Then the different manifestations of
inversion in relation to the general solution, an arbitrary analytical
function inside and the core of the coefficient are examined. It shows that
all the major problems of the Vekua equation theories, including boundary
value problems can be interpreted and solved using the principle of
inversion. The main significance of the fundamentally finite integrable
Vekua equation is that the real and imaginary part of the solution can be
separated, which in many mechanical and technique problems have certain
physical meanings.
Non-autonomous boundary value problems on the real line
