  Using the pfaffian structure of the generating series for locally orientable
maps, we show that the generating series satsifies a nonlinear differential
equation called the BKP equation. Using this we are able to derive a cubic
differential equation which is satisfied by the generating series for locally
orientable triangulations. As a result, we prove a conjecture of Garoufalidis
and Mari\~no concerning the constant $p_g$ which appears in asymptotic formulas
for a variety of rooted maps on non-orientable surfaces. This allows one to
determine the asymptotic expansion for $p_g$ up to an unknown Stokes constant.
