  We give the exact construction of Riemannian (or stringy) instantons, which
are classical solutions of 2d Yang-Mills theories that interpolate between
initial and final string configurations. They satisfy the Hitchin equations
with special boundary conditions. For the case of U(2) gauge group those
equations can be written as the sinh-Gordon equation with a delta function
source. Using techniques of integrable theories based on the zero curvature
conditions, we show that the solution is a condensate of an infinite number of
one-solitons with the same topological charge and with all possible rapidities.
