An alternative approach uses the Zakharov–Shabat system directly and employs the following Darboux transformation: ϕ → ϕ = ϕ Λ − σ ϕ U → U = U + σ = φ Ω φ − 1 {\displaystyle {\begin{aligned}&\phi \to \phi =\phi \Lambda -\sigma \phi \\&U\to U=U+\\&\sigma =\varphi \Omega \varphi ^{-1}\end{aligned}}} which leaves the system invariant.
O abordare alternativă folosește direct sistemul Zaharov-Shabat și următoarea transformare Darboux: ϕ → ϕ = ϕ Λ − σ ϕ U → U = U + σ = φ Ω φ − 1 {\displaystyle {\begin{aligned}&\phi \to \phi =\phi \Lambda -\sigma \phi \\&U\to U=U+\\&\sigma =\varphi \Omega \varphi ^{-1}\end{aligned}}} care lasă invariant sistemul.