The local ill-posedness of the modified KdV equation

Björn Birnir; Gustavo Ponce; Nils Svanstedt

Annales de l'I.H.P. Analyse non linéaire (1996)

  • Volume: 13, Issue: 4, page 529-535
  • ISSN: 0294-1449

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Birnir, Björn, Ponce, Gustavo, and Svanstedt, Nils. "The local ill-posedness of the modified KdV equation." Annales de l'I.H.P. Analyse non linéaire 13.4 (1996): 529-535. <http://eudml.org/doc/78390>.

@article{Birnir1996,
author = {Birnir, Björn, Ponce, Gustavo, Svanstedt, Nils},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {local ill-posedness of the Cauchy problem; modified KdV equation},
language = {eng},
number = {4},
pages = {529-535},
publisher = {Gauthier-Villars},
title = {The local ill-posedness of the modified KdV equation},
url = {http://eudml.org/doc/78390},
volume = {13},
year = {1996},
}

TY - JOUR
AU - Birnir, Björn
AU - Ponce, Gustavo
AU - Svanstedt, Nils
TI - The local ill-posedness of the modified KdV equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1996
PB - Gauthier-Villars
VL - 13
IS - 4
SP - 529
EP - 535
LA - eng
KW - local ill-posedness of the Cauchy problem; modified KdV equation
UR - http://eudml.org/doc/78390
ER -

References

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  1. [1] Batemann Manuscript Project, Tables of Integral Transforms, Vol. IMc Graw-Hill, New York, 1954. 
  2. [2] B. Bimir, Kenig C.E., Ponce G., Svanstead N. and Vega L., On the ill-posedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations, to appear in the Journal of the London Math. Soc., 1996. Zbl0855.35112MR1347022
  3. [3] C.S. Gardner, Korteweg de Vries equation and generalizations IV. The Korteweg de Vries equation as a Hamiltonian system, J. Math. Phys., Vol. 12, 1971, pp. 1548-1551. Zbl0283.35021MR286402
  4. [4] R.T. Glassey, On the blowing-up solutions to the Cauchy problem for nonlinear Schrödinger equations, J. Math. Phys., Vol. 18, 1979, pp. 1794-1797. Zbl0372.35009MR460850
  5. [5] C.S. Gardner, T.H. Greene, M.D. Kruskal and R.M. Miura, Methods for solving the Korteweg-de Vries equation, Physical Review Letters, Vol. 19, 1967, pp. 1095-1097. Zbl1061.35520
  6. [6] C.E. Kenig, G. Ponce and L. Vega, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via contraction principle, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 527-620. Zbl0808.35128MR1211741
  7. [7] R.M. Miura, Korteweg-de Vries equation and generalizations I. A remarkable explicit nonlinear transformation, J. Math. Phys., Vol. 9, 1968, pp. 1202-1204. Zbl0283.35018MR252825
  8. [8] J. Rauch, Nonlinear superposition and absorption of delta waves in one space dimension, J. Funct. Anal., Vol. 73, 1987, pp. 152-178. Zbl0661.35058MR890661

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