Geodesic
Regularizing the KdV Equation near a Blow-Up Surface
Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 3, pp. 394-400

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We propose a method for regularizing the Korteweg–de Vries equation near, rather than on, a blow-up surface. This allows showing that for sufficiently small initial data at $x=0$, a blow-up surface exists nearby and is an analytic manifold. 
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     author = {N. Joshi},
     title = {Regularizing the {KdV} {Equation} near a {Blow-Up} {Surface}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {394--400},
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     volume = {127},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_127_3_a5/}
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N. Joshi. Regularizing the KdV Equation near a Blow-Up Surface. Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 3, pp. 394-400. http://geodesic.mathdoc.fr/item/TMF_2001_127_3_a5/