Results on qualitative features of periodic solutions of KdV

T. Kappeler; B. Schaad; P. Topalov

doi:10.5802/slsedp.3

T. Kappeler ; B. Schaad ; P. Topalov

Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exposé no. 3, 7 p.

EuDML MR

DOI : 10.5802/slsedp.3

@article{SLSEDP_2011-2012____A3_0,
     author = {T. Kappeler and B. Schaad and P. Topalov},
     title = {Results on qualitative features of periodic solutions of {KdV}},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:3},
     pages = {1--7},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2011-2012},
     doi = {10.5802/slsedp.3},
     mrnumber = {3379844},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.3/}
}

TY  - JOUR
AU  - T. Kappeler
AU  - B. Schaad
AU  - P. Topalov
TI  - Results on qualitative features of periodic solutions of KdV
JO  - Séminaire Laurent Schwartz — EDP et applications
N1  - talk:3
PY  - 2011-2012
SP  - 1
EP  - 7
PB  - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.3/
DO  - 10.5802/slsedp.3
LA  - en
ID  - SLSEDP_2011-2012____A3_0
ER  -

%0 Journal Article
%A T. Kappeler
%A B. Schaad
%A P. Topalov
%T Results on qualitative features of periodic solutions of KdV
%J Séminaire Laurent Schwartz — EDP et applications
%Z talk:3
%D 2011-2012
%P 1-7
%I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
%U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.3/
%R 10.5802/slsedp.3
%G en
%F SLSEDP_2011-2012____A3_0

T. Kappeler; B. Schaad; P. Topalov. Results on qualitative features of periodic solutions of KdV. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exposé no. 3, 7 p. doi : 10.5802/slsedp.3. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.3/

Bibliographie
Cité par

[1] M. Erdogan, N. Tzirakis, V. Zharnitsky : Near-linear dynamics in KdV with periodic boundary conditions, Nonlinearity 23 (2010), 1675-1694. | MR | Zbl

[2] B. Grébert, T. Kappeler, J. Pöschel: Normal form theory of the NLS equation, preliminary version, arxiv.org/abs/0907.3938v1 2009. To appear in EMS Series of Lectures in Mathematics, EMS Publishing House.

[3] A. Its, V. Matveev : A class of solutions of the Korteweg-de Vries equation(in Russian), Problems in Math. Physics N08, Izdat. Leningrad Univ., Leningrad, 1976 , 79-92. | MR

[4] T. Kappeler: Fibration of the phase-space for the Korteweg-de Vries equation, Ann. Inst. Fourier 41 (1991), 539-575. | Numdam | MR | Zbl

[5] T. Kappeler, M. Makarov: On action-angle variables for the second Poisson bracket, Comm. in Math. Phys., 214, 3 (2000), 651-677. | MR | Zbl

[6] T. Kappeler, M. Makarov: On Birkhoff coordinates for KdV, Ann. H. Poincaré 2 (2001), 807 - 856. | MR | Zbl

[7] T. Kappeler, J. Pöschel: KdV & KAM, Ergebnisse Math. u. Grenzgebiete, Springer, Berlin, 2003. | MR

[8] T. Kappeler, B. Schaad, P. Topalov: mKdV and its Birkhoff coordinates, Physica D: Nonlinear Phenomena, 237, 10-12 (2008), 1655-1662. | MR | Zbl

[9] T. Kappeler, B. Schaad, P. Topalov: Asymptotic estimates of spectral quantities of Schrödinger operators, arXiv: 1107.4542.

[10] T. Kappeler, B. Schaad, P. Topalov: Qualitative features of periodic solutions of KdV, arXiv: 1110.0455.

[11] T. Kappeler, P. Topalov: Global fold structure of the Miura map on $L^{2} (𝕋, ℝ)$ , Int. Math. Research Notices (2004), 2039-2068. | MR | Zbl

[12] T. Kappeler, P. Topalov: Global wellposedness of KdV in $H^{- 1} (𝕋, ℝ)$ , Duke Math. J. 135 (2006), 327-360. | MR | Zbl

[13] S. Kuksin: Damped driven KdV and effective equation for long-time behaviour of its solution, preliminary version, 2009. | MR

[14] S. Kuksin, G. Perelman: Vey theorem in infinite dimensions and its application to KdV, Discrete and Continuous Dynamical Systems Ser. A, 27, no 1, (2010), 1-24. | MR | Zbl

[15] S. Kuksin, A. Piatnitski: Khasminskii - Whitham averaging for randomly perturbated KdV equation, J. Math. Pures Appl. 89 (2008), 400-428. | MR | Zbl

[16] V. Marchenko: Sturm-Liouville operators and applications, Birkhäuser, Basel, 1986. | MR | Zbl

[17] H. McKean, E. Vaninsky: Action-angle variables for the cubic Schroedinger equation, Comm. Pure Appl. Math. 50 (1997), 489-562. | MR | Zbl

[18] A. Savchuk, A. Shkalikov: On the eigenvalues of the Sturm-Liouville operator with potentials from Sobolev spaces, Math. Notes 80, no 6 (2006), 864-884. | MR | Zbl

[19] B. Schaad: Qualitative features of periodic solutions of KdV, PhD thesis, University of Zurich, 2011.

Cité par Sources :