@article{AIHPC_2009__26_3_917_0, author = {Hadac, Martin and Herr, Sebastian and Koch, Herbert}, title = {Well-Posedness and {Scattering} for the {KP-II} {Equation} in a {Critical} {Space}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {917--941}, publisher = {Elsevier}, volume = {26}, number = {3}, year = {2009}, doi = {10.1016/j.anihpc.2008.04.002}, mrnumber = {2526409}, zbl = {1169.35372}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2008.04.002/} }
TY - JOUR AU - Hadac, Martin AU - Herr, Sebastian AU - Koch, Herbert TI - Well-Posedness and Scattering for the KP-II Equation in a Critical Space JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 917 EP - 941 VL - 26 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2008.04.002/ DO - 10.1016/j.anihpc.2008.04.002 LA - en ID - AIHPC_2009__26_3_917_0 ER -
%0 Journal Article %A Hadac, Martin %A Herr, Sebastian %A Koch, Herbert %T Well-Posedness and Scattering for the KP-II Equation in a Critical Space %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 917-941 %V 26 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2008.04.002/ %R 10.1016/j.anihpc.2008.04.002 %G en %F AIHPC_2009__26_3_917_0
Hadac, Martin; Herr, Sebastian; Koch, Herbert. Well-Posedness and Scattering for the KP-II Equation in a Critical Space. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 3, pp. 917-941. doi : 10.1016/j.anihpc.2008.04.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2008.04.002/
[1] Elastic and Inelastic Line-Soliton Solutions of the Kadomtsev-Petviashvili II Equation, Math. Comput. Simulation 74 (2-3) (2007) 237-250. | MR | Zbl
, ,[2] On the Cauchy Problem for the Kadomtsev-Petviashvili Equation, Geom. Funct. Anal. 3 (4) (1993) 315-341. | MR | Zbl
,[3] Asymptotics, Frequency Modulation, and Low Regularity Ill-Posedness for Canonical Defocusing Equations, Amer. J. Math. 125 (6) (2003) 1235-1293. | MR | Zbl
, , ,[4] Soliton Equations and Hamiltonian Systems, Advanced Series in Mathematical Physics, vol. 26, second ed., World Scientific Publishing Co. Inc., River Edge, NJ, 2003. | MR | Zbl
,[5] Geometric Measure Theory, Reprint of the 1969 edition, Classics in Mathematics, Springer-Verlag, Berlin, 1996. | MR | Zbl
,[6] On the Cauchy Problem for the Zakharov System, J. Funct. Anal. 151 (2) (1997) 384-436. | MR | Zbl
, , ,[7] M. Hadac, Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations, Trans. Amer. Math. Soc., in press. | MR | Zbl
[8] Global Solution for the Kadomtsev-Petviashvili Equation (KPII) in Anisotropic Sobolev Spaces of Negative Indices, Electron. J. Differential Equations 68 (2003), 12 pp. (electronic). | MR | Zbl
, ,[9] On the Stability of Solitary Waves in Weakly Dispersing Media, Sov. Phys. Dokl. 15 (1970) 539-541. | Zbl
, ,[10] Local Well Posedness for Modified Kadomstev-Petviashvili Equations, Differential Integral Equations 18 (10) (2005) 1111-1146. | MR
, ,[11] Asymptotics of Solutions of Multidimensional Integrable Equations and Their Perturbations, J. Math. Sci., New York 138 (6) (2006) 6067-6230, Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya, vol. 11, Differential Equations, 2004. | MR
,[12] Dispersive Estimates for Principally Normal Pseudodifferential Operators, Comm. Pure Appl. Math. 58 (2) (2005) 217-284. | MR | Zbl
, ,[13] A Priori Bounds for the 1D Cubic NLS in Negative Sobolev Spaces, Internat. Math. Res. Notices 2007 (2007), article ID rnm053, 36 pages. | MR | Zbl
, ,[14] Asymptotic Stability of Solitons of the Subcritical GKdV Equations Revisited, Nonlinearity 18 (1) (2005) 55-80. | MR | Zbl
, ,[15] New Thoughts on Besov Spaces, Duke University Mathematics Series. I, Mathematics Department, Duke University, Durham, 1976, 305 p. | MR | Zbl
,[16] F. Rousset, N. Tzvetkov, Transverse nonlinear instability for two-dimensional dispersive models, Ann. I. H. Poincaré - AN (2008), in press, doi: 10.1016/j.anihpc.2007.09.006. | Numdam | MR | Zbl
[17] Remarks on the Generalized Kadomtsev-Petviashvili Equations, Indiana Univ. Math. J. 42 (3) (1993) 1011-1026. | MR | Zbl
,[18] Degenerative Dispersion Laws, Motion Invariants and Kinetic Equations, Physica D 1 (2) (1980) 192-202. | MR
, ,[19] Well-Posedness for the Kadomtsev-Petviashvili II Equation, Adv. Differential Equations 5 (10-12) (2000) 1421-1443. | MR | Zbl
,[20] On the Local Regularity of the Kadomtsev-Petviashvili-II Equation, Internat. Math. Res. Notices 2001 (2) (2001) 77-114. | MR | Zbl
, ,[21] Scattering for the Quartic Generalised Korteweg-De Vries Equation, J. Differential Equations 232 (2) (2007) 623-651. | MR | Zbl
,[22] On the Cauchy Problem for Kadomtsev-Petviashvili Equation, Comm. Partial Differential Equations 24 (7-8) (1999) 1367-1397. | MR | Zbl
,[23] Local Solutions of the Kadomtsev-Petviashvili Equation, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (2) (1989) 193-209. | MR | Zbl
,[24] The Quadratic Variation of a Function and Its Fourier Coefficients, in: (Ed.), Collected Works With Commentaries. Volume II: Generalized Harmonic Analysis and Tauberian Theory; Classical Harmonic and Complex Analysis, Mathematicians of Our Time, vol. 15, The MIT Press, Cambridge, MA - London, 1979, (1924), XIII, 969 p. | MR | Zbl
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