  From a specific series of exchange conditions for a one-parameter Hamiltonian
vector field, we establish an integrable hierarchy using Lax pairs derived from
the dispersionless partial differential equation. An exterior differential form
of the integrable hierarchy is introduced, further confirming the existence of
the tau function. Subsequently, we present the twistor structure of the
hierarchy. By constructing the nonlinear Riemann Hilbert problem for the
equation, the structure of the solution to the equation is better understood.
