Construction de solutions pour les équations de Korteweg-de Vries généralisées

Raphaël Côte

Séminaire Équations aux dérivées partielles (2006-2007)

  • Volume: 2006-2007, page 1-17

How to cite

top

Côte, Raphaël. "Construction de solutions pour les équations de Korteweg-de Vries généralisées." Séminaire Équations aux dérivées partielles 2006-2007 (2006-2007): 1-17. <http://eudml.org/doc/11159>.

@article{Côte2006-2007,
author = {Côte, Raphaël},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {inverse scattering; linear scattering; solitons; generalized Korteweg-de Vries equation},
language = {fre},
pages = {1-17},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Construction de solutions pour les équations de Korteweg-de Vries généralisées},
url = {http://eudml.org/doc/11159},
volume = {2006-2007},
year = {2006-2007},
}

TY - JOUR
AU - Côte, Raphaël
TI - Construction de solutions pour les équations de Korteweg-de Vries généralisées
JO - Séminaire Équations aux dérivées partielles
PY - 2006-2007
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2006-2007
SP - 1
EP - 17
LA - fre
KW - inverse scattering; linear scattering; solitons; generalized Korteweg-de Vries equation
UR - http://eudml.org/doc/11159
ER -

References

top
  1. Michael Christ and Michael I. Weinstein, Dispersion of small amplitudes solutions of the generalized Korteweg-de Vries equation, J. Funct. Anal. 100 (1991), 87–109. Zbl0743.35067MR1124294
  2. Raphaël Côte, Construction of solutions to the L 2 -critical KdV equation with a given asymptotic behaviour, Duke Math. J., to appear. Zbl1130.35112MR2322685
  3. —, Construction of solutions to the subcritical gKdV equations with a given asymptotical behaviour, J. Funct. Anal. (2006), no. 241, 143–211. Zbl1157.35091MR2264249
  4. —, Large data wave operator for the generalized Korteweg-de Vries equations, Differential Integral Equations 19 (2006), no. 2, 163–188. Zbl1212.35408MR2194502
  5. Wiktor Eckhaus and Peter Schuur, The emergence of solutions of the Korteweg-de Vries equation form arbitrary initial conditions, Math. Methods Appl. Sci. 5 (1983), 97–116. Zbl0518.35074MR690898
  6. Nakao Hayashi and Pavel I. Naumkin, Large time asymptotics of solutions to the generalized Korteweg-De Vries equation, J. Funct. Anal. 159 (1998), 110–136. Zbl0915.35093MR1654178
  7. Carlos E. Kenig, Gustavo Ponce, and Luis Vega, Well-posedness and scattering result for the generalized Korteweg-De Vries equation via contraction principle, Comm. Pure Appl. Math. 46 (1993), 527–620. Zbl0808.35128MR1211741
  8. —, On the concentration of blow up solutions for the generalized KdV equation critical in L 2 , Nonlinear wave equations (Providence, RI, 1998), Contemp. Math., vol. 263, Amer. Math. Soc., Providence, RI, 2000, pp. 131–156. Zbl0970.35125MR1777639
  9. Yvan Martel, Asymptotic N -soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations, Amer. J. Math. 127 (2005), no. 5, 1103–1140. Zbl1090.35158MR2170139
  10. Yvan Martel and Frank Merle, A Liouville theorem for the critical generalized Korteweg-de Vries equation, J. Math. Pures Appl. (9) 79 (2000), 339–425. Zbl0963.37058MR1753061
  11. —, Asymptotic stability of solitons for subcritical generalized KdV equations., Arch. Ration. Mech. Anal. 157 (2001), no. 3, 219–254. Zbl0981.35073MR1826966
  12. —, Blow up in finite time and dynamics of blow up solutions for the L 2 -critical generalized KdV equations, J. Amer. Math. Soc. 15 (2002), 617–664. Zbl0996.35064MR1896235
  13. —, Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized kdv equation, Ann. of Math. (2) 1 (2002), 235–280. Zbl1005.35081MR1888800
  14. Yvan Martel, Frank Merle, and Tai-Peng Tsai, Stability and asymptotic stability in the energy space of the sum of n solitons for subcritical gKdV equations, Comm. Math. Phys. 231 (2002), 347–373. Zbl1017.35098MR1946336
  15. Frank Merle, Existence of blow-up solutions in the energy space for the critical generalized Korteweg-de Vries equation, J. Amer. Math. Soc. 14 (2001), 555–578. Zbl0970.35128MR1824989
  16. Robert M. Miura, The Korteweg-de Vries equation : a survey of results, SIAM Rev. 18 (1976), 412–459. Zbl0333.35021MR404890
  17. Gustavo Ponce and Luis Vega, Nonlinear small data scattering for the generalized Korteweg-de Vries equation, J. Funct. Anal. 90 (1990), 445–457. Zbl0771.35062MR1052343
  18. Mohammed A. Rammaha, On the asymptotic behavior of solutions of generalized Korteweg-de Vries equation, J. Math. Anal. Appl. 140 (1989), no. 1, 228–240. Zbl0686.35018MR997853
  19. Peter Cornelis Schuur, Asymptotic analysis of soliton problems, Lecture Notes in Mathematics, vol. 1232, Springer-Verlag, Berlin, 1986, An inverse scattering approach. Zbl0643.35003MR874343
  20. Walter A. Strauss, Dispersion of low-energy waves for two conservative equations, Arch. Ration. Mech. Anal. 55 (1974), 86–92. Zbl0289.35048MR352743

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.