  Evidently, the linear superposition principle can not be exactly established
as a general principle in the presence of nonlinearity, and, at the first
glance, there is no expectation for it to hold even approximately. In this
letter, it is shown that the balance of different nonlinear effects describes
what linear superpositions may occur in nonlinear systems. The heavenly
equations are of significance in several scientific fields, especially in
relativity, gravity, field theory, and fluid dynamics. A special type of
implicit shock wave solution with three two-dimensional arbitrary functions of
the general heavenly equation is revealed. Restrict the two-dimensional
arbitrary functions to some types of one-dimensional arbitrary functions, it is
found that the nonlinear effects can be balanced such that the "impossible"
linear superposition solutions can be nontrivially constituted to new solutions
of the general heavenly equation.
