initial conditions

[ballzac]

Hi,

I have a problem that I am working through, and I am at a point where I'm not sure what to do.

I am solving a PDE using the method of characteristics. This has given me the solution

ϕ(x,t)=F(x+(3ϕ^2-1)t) "for any function " F

I have the initial conditions

ϕ(x,0)=1, x<0
and
ϕ(x,0)=0, x>0

Normally I have no trouble using initial conditions, but this has me stumped. I set t=0 and phi=1 (or 0), and I get F(x)=0, 1

I have no idea what to do with this. Normally I would end up with something like F(x)=sin(x), and then I could say

ϕ(x,t)=sin(x+(3ϕ^2-1)t)

but that isn't the case her. Any help would be much appreciated.