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The Vakhitov–Kolokolov stability criterion is a condition for linear stability (sometimes called spectral stability) of solitary wave solutions to a wide class of Hamiltonian systems, named after Soviet scientists Aleksandr Kolokolov (Александр Александрович Колоколов) and Nazib Vakhitov (Назиб Галиевич Вахитов).The condition for linear stability of a solitary wave with frequency has the form where is the charge (or momentum) of the solitary wave,conserved by Noether's theorem due to U(1)-invariance of the system.
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