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• W2949568314 abstract "The Miura map (introduced by Miura) is a nonlinear map between function spaces which transforms smooth solutions of the modified Korteweg - de Vries equation (mKdV) to solutions of the Korteweg - de Vries equation (KdV). In this paper we study relations between the Miura map and Schroedinger operators with real-valued distributional potentials (possibly not decaying at infinity) from various spaces. We also investigate mapping properties of the Miura map in these spaces. As an application we prove existence of solutions of the Korteweg - de Vries equation in the negative Sobolev space H^{-1} for the initial data in the range of the Miura map." @default.
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• W2949568314 date "2005-06-20" @default.
• W2949568314 modified "2023-09-27" @default.
• W2949568314 title "The Miura Map on the Line" @default.
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