Isospectral flows of third order operators

We consider the third order linear differential operator L-p,L-q = i d(3)/d x(3) + i d/dx q + iq d/dx + p on the unit interval. The associated boundary conditions are y(0) = y(1) = 0, y'(0) = zy'(1) with z is an element of C, \z\ = 1. For all but a finite number of parameters z, the eigenvalues lambd a (j) of L-p,L-q are of multiplicity one. For fixed boundary conditions we make the formulae for isospectral flows induced by the Hamiltonian function lambda (j) explicit. These flows commute.