Generalizations of the KPZ equation (minor changes to enable easy latexing)
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We generalize the KPZ equation to an O(3) $N=2j+1$ component model. In the limit $N \to \infty$ we show that the mode coupling equations become exact. Solving these approximately we find that the dynamic exponent $z$ increases from $3/2$ for $d=1$ to $2$ at the dimension $d\approx3.6$. For $d=1$ it can be shown analytically that $z=3/2$ for all $j$. The case $j=2$ for $d=2$ is investigated by numerical integration of the KPZ equation.
12 pages + 2 figures available on request, LaTeX version 3.1
12 pages + 2 figures available on request, LaTeX version 3.1