An exact representation of N-wave solutions for the non-planar Burgers equation
u
t
+ uu
x
+ ½ju/t = ½δu
xx
,
j = m/n, m < 2n
, where
m
and
n
are positive integers with no common factors, is given. This solution is asymptotic to the inviscid solution for |
x
| < √(2
Q
0
t
), where
Q
0
is a function of the initial lobe area, as lobe Reynolds number tends to infinity, and is also asymptotic to the old age linear solution, as
t
tends to infinity; the formulae for the lobe Reynolds numbers are shown to have the correct behaviour in these limits. The general results apply to all
j = m/n, m < 2n
, and are rather involved; explicit results are written out for
j
= 0, 1, ½, 1/3 and 1/4. The case of spherical symmetry
j
= 2 is found to be ‘singular’ and the general approach set forth here does not work; an alternative approach for this case gives the large time behaviour in two different time regimes. The results of this study are com pared with those of Crighton & Scott (1979).
Exact N
-Wave Solutions of Generalized Burgers Equations