The transverse displacement $$y(x,t)$$ of a wave on a string is given by $$y(x,t) = e^{-(ax^2 + bt^2 + 2\sqrt{ab}\, xt)}$$. This represents a:

A

wave moving in $$-x$$ direction with speed $$\sqrt{\dfrac{b}{a}}$$

B

standing wave of frequency $$\sqrt{b}$$

C

standing wave of frequency $$\dfrac{1}{\sqrt{b}}$$

D

wave moving in $$+x$$ direction with speed $$\sqrt{\dfrac{a}{b}}$$