General approach to the electrostatic problem of the IDT in an external electric field

General exact solutions for finding the surface charge and electric field distributions in an arbitrary IDT with a limited number of electrodes and in an arbitrary periodic IDT with a complex unit cell are given. They are based on the Keldysh-Sedov solution to the special mixed boundary problem of the analytic function theory. The external electric field may arbitrarily vary along the structure. The solutions may be expressed as a linear combination of potential differences between the electrodes and of integrals containing the external electric field. These solutions may be transformed for the description of any electrode connection conditions.