  The formula of expanding the Abel variety theta function restricted to Abel
subvariety into theta functions of this subvariety is obtained. With the help
of this formula the solution of differential equations with Jacobi theta
functions, restricted on a nonprincipally polarized Abel subvariety and their
translations are rewritten in terms of the theta functions of these
subvarieties. This is exemplified by the CKP equations, the Bogoyavlenskij
system, and the Toda $g_2^{(1)}$-chain.
