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

General equation of traveling wave is $y=f(ax\pm bt)=f(x\pm vt)$

$\therefore \mathrm{y}={\mathrm{e}}^{-({\mathrm{ax}}^2+{\mathrm{bt}}^2+2\sqrt{\mathrm{ab}}\mathrm{xt})}={\mathrm{e}}^{-{(\sqrt{\mathrm{a}}\mathrm{x}+\sqrt{\mathrm{b}}\mathrm{t})}^2}$

So, the wave will be traveling along –x axis with speed $\sqrt{\frac{b}{a}}$.