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Mosc. Math. J., 2001, Volume 1, Number 4, Pages 491–520 (Mi mmj33)  

This article is cited in 6 scientific papers (total in 7 papers)

On solutions for the Kadomtsev–Petviashvili I equation

J. E. Colliandera, C. E. Kenigb, G. Staffilanicd

a University of Toronto
b University of Chicago
c Stanford University
d Brown University

Abstract: Oscillatory integral techniques are used to study the well-posedness of the KP-I equation for initial data that are small with respect to the norm of a weighted Sobolev space involving derivatives of total order no larger than 2.

Key words and phrases: Kadomtsev–Petviashvili equation, initial value problem, well-posedness, oscillatory intergals.

DOI: https://doi.org/10.17323/1609-4514-2001-1-4-491-520

Full text: http://www.ams.org/.../abst1-4-2001.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 35Q53, 35D25
Received: November 2, 2001; in revised form December 3, 2001
Language:

Citation: J. E. Colliander, C. E. Kenig, G. Staffilani, “On solutions for the Kadomtsev–Petviashvili I equation”, Mosc. Math. J., 1:4 (2001), 491–520

Citation in format AMSBIB
\Bibitem{ColKenSta01}
\by J.~E.~Colliander, C.~E.~Kenig, G.~Staffilani
\paper On solutions for the Kadomtsev--Petviashvili~I equation
\jour Mosc. Math.~J.
\yr 2001
\vol 1
\issue 4
\pages 491--520
\mathnet{http://mi.mathnet.ru/mmj33}
\crossref{https://doi.org/10.17323/1609-4514-2001-1-4-491-520}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1901072}
\zmath{https://zbmath.org/?q=an:1002.35108}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208587600002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    Erratum

    This publication is cited in the following articles:
    1. Colliander J., Kenig C., Staffilani G., “Low regularity solutions for the Kadomtsev-Petviashvili I equation”, Geom. Funct. Anal., 13:4 (2003), 737–794  crossref  mathscinet  zmath  isi
    2. J. E. Colliander, C. E. Kenig, G. Staffilani, “Errata: “On solutions for the Kadomtsev–Petviashvili I equation””, Mosc. Math. J., 4:2 (2004), 529–530  mathnet  crossref  mathscinet
    3. Kenig C.E., “On the local and global well-posedness theory for the KP-I equation”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 21:6 (2004), 827–838  crossref  mathscinet  zmath  adsnasa  isi
    4. Abounouh M., Goubet O., “Regularity of the attractor for KP1-burgers equation: the periodic case”, Commun. Pure Appl. Anal., 3:2 (2004), 237–252  crossref  mathscinet  zmath  isi
    5. Chen R.M., “The Cauchy problem and the stability of solitary waves of a hyperelastic dispersive equation”, Indiana Univ. Math. J., 57:5 (2008), 2377–2421  crossref  mathscinet  zmath  isi
    6. Chen Wengu, Li Junfeng, Miao Changxing, “On the low regularity of the fifth order Kadomtsev-Petviashvili I equation”, J. Differential Equations, 245:11 (2008), 3433–3469  crossref  mathscinet  zmath  isi
    7. Linares F., Pastor A., “Well-posedness for the two-dimensional modified Zakharov-Kuznetsov equation”, SIAM J. Math. Anal., 41:4 (2009), 1323–1339  crossref  mathscinet  zmath  isi
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