Is \(y=Ae^{-x-t^2}\) a wave?
I'm testing it by using the wave equation:\[\frac{\partial ^2}{\partial x^2}=\frac{1}{u^2} \frac{\partial ^2}{\partial t^2}\]So I currently have\[\frac{\partial ^2}{\partial x^2}=Ae^{-x-t^2}\]and\[\frac{\partial ^2}{\partial t^2}=Ae^{-x-t^2} [-2+4t^2]\]Normally, a wave has the form \(kx-\omega t\), and the velocity can be calculated from that, but this one has a \(t^2\), which confuses me. Any thoughts?

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Those derivatives should all be with respect to y also.

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