I find many references to the "N-soliton" solution to the KdV equation
$$ u_{t} - uu_{x} + u_{xxx} = 0 $$
of the form $u(x, 0) = N(N+1) \operatorname{sech}^{2}(x)$. However, I require the $N$ soliton solution for
$$ u_{t} + uu_{x} + u_{xxx} = 0 $$ instead. Does anyone know the answer or know a paper where this is found?