Exact Travelling Wave Solutions of Discrete Planar Velocity Boltzmann Models

By investigating the discrete planar Boltzmann models: the square 4-velocity and the hexagonal 6-velocity models, exact travelling wave solutions can be studied in a concise way. And their exact travelling wave solutions can only be monotonic travelling wave . The conclusions of the precursors need ameliorating. This suggests a general method for obtaining nontrivial exact solutions for the similar discrete Boltzmann equation.