N soliton solution KdV equation

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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?