Orbital Stability of KdV Multisolitons in $$H^{-1}$$

We prove that multisoliton solutions of the Korteweg–de Vries equation are orbitally stable in \(H^{-1}(\mathbb {R})\). introduce a variational characterization multisolitons remains meaningful at such low regularity and show all optimizing sequences converge to manifold multisolitons. The proximity required initial time is uniform across entire multisolitons; this had not been demonstrated previously, even \(H^1\).