Geodesic
The Korteweg–de Vries equation at H -1 regularity
Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 5, pp. 1071-1098

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In this paper we will prove the existence of weak solutions to the Korteweg–de Vries initial value problem on the real line with H -1 initial data; moreover, we will study the problem of orbital and asymptotic H s stability of solitons for integers s≥-1; finally, we will also prove new a priori H -1 bound for solutions to the Korteweg–de Vries equation. The paper will utilise the Miura transformation to link the Korteweg–de Vries equation to the modified Korteweg–de Vries equation.

DOI : 10.1016/j.anihpc.2014.05.004
Keywords: Korteweg–de Vries equation, Stability of solitons, Miura map 
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     author = {Buckmaster, Tristan and Koch, Herbert},
     title = {The {Korteweg{\textendash}de} {Vries} equation at $ {H}^{-1}$ regularity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1071--1098},
     publisher = {Elsevier},
     volume = {32},
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     year = {2015},
     doi = {10.1016/j.anihpc.2014.05.004},
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     zbl = {1331.35300},
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     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.05.004/}
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Buckmaster, Tristan; Koch, Herbert. The Korteweg–de Vries equation at $ {H}^{-1}$ regularity. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 5, pp. 1071-1098. doi: 10.1016/j.anihpc.2014.05.004

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