Cnoidal waves of KdV are nonlinearly modulationally stable under localized H^3 perturbations, the first such result for non-reducible periodic waves in Hamiltonian systems.
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Nonlinear stability of periodic waves in the Korteweg-de Vries equation under localized perturbations
Cnoidal waves of KdV are nonlinearly modulationally stable under localized H^3 perturbations, the first such result for non-reducible periodic waves in Hamiltonian systems.