ABSTRACT
This is a special case of equation 6.4.2.1 with f (w) = cwp. 1◦. Suppose w(x, y, t) is a solution of the equation in question. Then the function
w1 = C1w ( C p-1 2-n
1 y, C p-1 1 t + C2
) ,
where C1 and C2 are arbitrary constants, is also a solution of the equation. 2◦. There are “two-dimensional” solutions of the following forms:
w(x, y, t) = U (r, t), r2 = x 2-n
a(2 – n)2 + y2-m
b(2 – m)2 ;
w(x, y, t) = t 1
1-p V (z1, z2), z1 = xt 1 n-2 , z2 = yt
2. ∂w
∂t =
∂
∂x
( axn
∂w
∂x
) + ∂
∂y
( beλy
∂w
∂y
) + cwp.
