@article{AIHPC_2009__26_3_841_0, author = {Kappeler, Thomas and P\"oSchel, J\"uRgen}, title = {On the {Periodic} {KdV} {Equation} in {Weighted} {Sobolev} {Spaces}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {841--853}, publisher = {Elsevier}, volume = {26}, number = {3}, year = {2009}, doi = {10.1016/j.anihpc.2008.03.004}, mrnumber = {2526404}, zbl = {1177.35199}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2008.03.004/} }
TY - JOUR AU - Kappeler, Thomas AU - PöSchel, JüRgen TI - On the Periodic KdV Equation in Weighted Sobolev Spaces JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 841 EP - 853 VL - 26 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2008.03.004/ DO - 10.1016/j.anihpc.2008.03.004 LA - en ID - AIHPC_2009__26_3_841_0 ER -
%0 Journal Article %A Kappeler, Thomas %A PöSchel, JüRgen %T On the Periodic KdV Equation in Weighted Sobolev Spaces %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 841-853 %V 26 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2008.03.004/ %R 10.1016/j.anihpc.2008.03.004 %G en %F AIHPC_2009__26_3_841_0
Kappeler, Thomas; PöSchel, JüRgen. On the Periodic KdV Equation in Weighted Sobolev Spaces. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 3, pp. 841-853. doi : 10.1016/j.anihpc.2008.03.004. http://www.numdam.org/articles/10.1016/j.anihpc.2008.03.004/
[1] Rational and Elliptic Solutions of the Korteweg-De Vries Equation and a Related Many-Body Problem, Comm. Pure Appl. Math 30 (1977) 95-148. | MR | Zbl
, , ,[2] On the Symplectic Structure of the Phase Space for Periodic KdV, Toda, and Defocusing NLS, Duke Math. J. 79 (1995) 549-604. | MR | Zbl
, , , ,[3] On the Korteweg-De Vries Equation: Frequencies and Initial Value Problem, Pacific J. Math 181 (1997) 1-55. | MR | Zbl
, , ,[4] Algebraic Lower Bounds for the Uniform Radius of Spatial Analyticity for the Generalized KdV Equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005) 783-797. | Numdam | MR | Zbl
, , ,[5] The Initial-Value Problem for the Korteweg-De Vries Equation, Philos. Trans. Roy. Soc. London Ser. A 278 (1975) 555-601. | MR | Zbl
, ,[6] Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations, II: the KdV-Equation, Geom. Funct. Anal. 3 (1993) 209-262. | MR | Zbl
,[7] On the Cauchy Problem for Periodic KdV-Type Equations, J. Fourier Anal. Appl. Special Issue (1995) 17-86. | MR | Zbl
,[8] Periodic Korteweg-De Vries Equation With Measures as Initial Data, Selecta Math. (N.S.) 3 (1997) 115-159. | MR | Zbl
,[9] Global Solutions of Nonlinear Schrödinger Equations, Amer. Math. Soc. Colloq. Publ., American Mathematical Society, Providence, RI, 1999. | MR | Zbl
,[10] Sharp Global Well-Posedness for KdV and Modified KdV on and , J. Amer. Math. Soc. 16 (2003) 705-749. | MR | Zbl
, , , , ,[11] Local and Global Well-Posedness for Non-Linear Dispersive and Wave Equations, www.math.ucla.edu/~tao/Dispersive.
, , , , ,[12] Smoothness of Schrödinger Operator Potential in the Case of Gevrey Type Asymptotics of the Gaps, J. Funct. Anal. 195 (2002) 89-128. | MR | Zbl
, ,[13] Spectral Triangles of Schrödinger Operators With Complex Potentials, Selecta Math. (N.S.) 9 (2003) 495-528. | MR | Zbl
, ,[14] Instability Zones of One-Dimensional Periodic Schrödinger and Dirac Operators, Uspekhi Mat. Nauk 61 (2006) 77-182, (in Russian). | MR | Zbl
, ,[15] Spectral Analysis of a Class of Second Order Nonselfadjoint Differential Operators, Funct. Anal. Appl. 14 (1980) 14-19. | MR | Zbl
,[16] A Note on Gaps of Hill's Equation, Int. Math. Res. Not. 50 (2004) 2703-2717. | MR | Zbl
, , ,[17] Local Well-Posedness of the Generalized Korteweg-De Vries Equation in Spaces of Analytic Functions, Differential Integral Equations 15 (2002) 1325-1334. | MR | Zbl
, ,[18] On the Birkhoff Coordinates for KdV, Ann. Henri Poincaré 2 (2001) 807-856. | MR | Zbl
, ,[19] Gap Estimates of the Spectrum of Hill's Equation and Action Variables for KdV, Trans. Amer. Math. Soc. 351 (1999) 619-646. | MR | Zbl
, ,[20] Estimates for Periodic and Dirichlet Eigenvalues of the Schrödinger Operator, SIAM J. Math. Anal. 33 (2001) 113-152. | MR | Zbl
, ,[21] KdV & KAM, Springer, Berlin, 2003. | MR
, ,[22] Global Wellposedness of KdV in , Duke Math. J. 135 (2006) 327-360. | MR | Zbl
, ,[23] On the Cauchy Problem for the Korteweg-De Vries Equation in Sobolev Spaces of Negative Indices, Duke Math. J. 71 (1993) 1-20. | MR | Zbl
, , ,[24] A Bilinear Estimate With Applications to the KdV Equation, J. Amer. Math. Soc. 9 (1996) 573-603. | MR | Zbl
, , ,[25] Perturbation Theory for Quasiperiodic Solutions of Infinite-Dimensional Hamiltonian Systems, and Its Application to the Korteweg-De Vries Equation, Mat. Sb. 136 (1988), (in Russian). English translation in, Math. USSR Sb. 64 (1989) 397-413. | MR | Zbl
,[26] Nearly Integrable Infinite-Dimensional Hamiltonian Systems, Lecture Notes in Mathematics, vol. 1556, Springer, 1993. | MR | Zbl
,[27] A Kam-Theorem for Equations of the Korteweg-De Vries Type, Rev. Math. Phys. 10 (1998) 1-64. | MR | Zbl
,[28] Analysis of Hamiltonian PDEs, Oxford University Press, Oxford, 2000. | MR | Zbl
,[29] A Characterization of the Spectrum of Hill's Operator, Math. USSR Sb. 97 (1975) 493-554. | Zbl
, ,[30] Problems and Theorems in Analysis I, Springer, New York, 1976. | Zbl
, ,[31] J. Pöschel, Hill's potential in weighted Sobolev spaces and their spectral gaps, Preprint, http://www.poschel.de/pbl.
[32] Inverse Spectral Theory, Academic Press, Boston, 1987. | MR | Zbl
, ,[33] On the Korteweg-De Vries Equation: Existence and Uniqueness, J. Math. Anal. Appl. 29 (1970) 569-579. | MR | Zbl
,[34] Sur Un Problème Non Linéaire, J. Math. Pures Appl. 48 (1969) 159-172. | MR | Zbl
,[35] Characterization of Hill Operators With Analytic Potentials, Integral Equations Operator Theory 41 (2001) 360-380. | MR | Zbl
,[36] The Inverse Problem for Periodic Potentials, Comm. Pure Appl. Math. 30 (1977) 321-342. | MR | Zbl
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