Is this a traveling wave?

[patm95]

1. The problem statement, all variables and given/known data

Is this a traveling wave? If so, find the speed and direction.

e^-(a^2y^2+b^2t^2-2abty)

2. Relevant equations

Probably relevant to know the differential wave equation.

3. The attempt at a solution

I have a feeling that this is a traveling wave as it is twice differentiable and appears to be a solution of the differential wave equation.

I first rearrange the equation to:

e^-(ay-bt)^2

So would this be a wave traveling right at speed b? I am unsure if it matters that I am keeping the sqaure in there?