On inversion in the case of the fundamentally finite integrable Vekua complex differential equation

Abstract

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.