  In this paper the travelling wave solutions in the adiabatic model with
two-step chain branching reaction mechanism are investigated both numerically
and analytically in the limit of equal diffusivity of reactant, radicals and
heat. The properties of these solutions and their stability are investigated in
detail. The behaviour of combustion waves are demonstrated to have similarities
with the properties of nonadiabatic one-step combustion waves in that there is
a residual amount of fuel left behind the travelling waves and the solutions
can exhibit extinction. The difference between the nonadiabatic one-step and
adiabatic two-step models is found in the behaviour of the combustion waves
near the extinction condition. It is shown that the flame velocity drops down
to zero and a standing combustion wave is formed as the extinction condition is
reached. Prospects of further work are also discussed.
