Nonaligned shocks for discrete velocity models of the Boltzmann equation

At the conclusion of I. Bonzani's presentation on the existence of structured shock solutions to the six-velocity, planar, discrete Boltzmann equation (with binary and triple collisions), Greenberg asked whether such solutions were possible in directions e(α)=(cosα ,sinα) when α was not one of the particle flow directions. This question generated a spirited discussion but the question was still open at the conclusion of the conference. In this note the author will provide a partial resolution to the question raised above. Using formal perturbation arguments he will produce approximate solutions to the equation considered by Bonzani which represent traveling waves propagating in any direction e(α)=(cosα ,sinα).