  We have recently solved the inverse spectral problem for integrable PDEs in
arbitrary dimensions arising as commutation of multidimensional vector fields
depending on a spectral parameter $\lambda$. The associated inverse problem, in
particular, can be formulated as a non linear Riemann Hilbert (NRH) problem on
a given contour of the complex $\lambda$ plane. The most distinguished examples
of integrable PDEs of this type, like the dispersionless
Kadomtsev-Petviashivili (dKP), the heavenly and the 2 dimensional
dispersionless Toda equations, are real PDEs associated with Hamiltonian vector
fields. The corresponding NRH data satisfy suitable reality and symplectic
constraints. In this paper, generalizing the examples of solvable NRH problems
illustrated in \cite{MS4,MS5,MS6}, we present a general procedure to construct
solvable NRH problems for integrable real PDEs associated with Hamiltonian
vector fields, allowing one to construct implicit solutions of such PDEs
parametrized by an arbitrary number of real functions of a single variable.
Then we illustrate this theory on few distinguished examples for the dKP and
heavenly equations. For the dKP case, we characterize a class of similarity
solutions, a class of solutions constant on their parabolic wave front and
breaking simultaneously on it, and a class of localized solutions breaking in a
point of the $(x,y)$ plane. For the heavenly equation, we characterize two
classes of symmetry reductions.
