Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation

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1. [1] Bona J.L., Dougalis V.A., Karakashian O.A., McKinney W.R., Conservative high-order numerical schemes for the generalized Korteweg–de Vries equation, Philos. Trans. Roy. Soc. London Ser. A351 (1995) 107-164. Zbl0824.65095MR1336983
2. [2] Bona J.L., Dougalis V.A., Karakashian O.A., McKinney W.R., Numerical simulation of singular solutions of the generalized Korteweg–de Vries equation, in: Dias F., Ghidaglia J.-M., Saut J.-C. (Eds.), Contemp. Math., vol. 200, Amer. Math. Soc., Providence, RI, 1996, pp. 17-29. Zbl0860.35112MR1410497
3. [3] Bona J.L., Grujić Z., Spatial analyticity for nonlinear waves, Math. Models Methods Appl. Sci.13 (2003) 1-15. Zbl1137.35418MR1977630
4. [4] Bona J.L., Weissler F.B., Similarity solutions of the generalized Korteweg–de Vries equation, Math. Proc. Cambridge Philos. Soc.127 (1999) 323-351. Zbl0939.35164MR1705463
5. [5] Bona J.L., Weissler F.B., Blow-up of spatially periodic complex-valued solutions of nonlinear dispersive equations, Indiana Univ. Math. J.50 (2001) 759-782. Zbl1330.35036MR1871389
6. [6] Bourgain J., Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Geom. Funct. Anal.3 (1993) 107-156, 209–262. Zbl0787.35098MR1215780
7. [7] de Bouard A., Hayashi N., Kato K., Gevrey regularizing effect for the (generalized) Korteweg–de Vries equation and nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire6 (1995) 673-715. Zbl0843.35098MR1360541
8. [8] Foias C., Temam R., Gevrey class regularity for the solutions of the Navier–Stokes equations, J. Funct. Anal.87 (1989) 359-369. Zbl0702.35203MR1026858
9. [9] Ginibre J., Tsutsumi Y., Velo G., On the Cauchy problem for the Zakharov system, J. Funct. Anal.151 (1997) 384-436. Zbl0894.35108MR1491547
10. [10] Grujić Z., Kalisch H., Local well-posedness of the generalized Korteweg–de Vries equation in spaces of analytic functions, Differential Integral Equations15 (2002) 1325-1334. Zbl1031.35124MR1920689
11. [11] Hayashi N., Analyticity of solutions of the Korteweg–de Vries equation, SIAM J. Math. Anal.22 (1991) 1738-1743. Zbl0742.35056MR1129407
12. [12] Hayashi N., Solutions of the (generalized) Korteweg–de Vries equation in the Bergman and Szegö spaces on a sector, Duke Math. J.62 (1991) 575-591. Zbl0729.35119MR1104808
13. [13] Kato T., Quasilinear equations of evolution with applications to partial differential equations, in: Lecture Notes in Math., vol. 448, Springer-Verlag, 1975, pp. 25-70. Zbl0315.35077MR407477
14. [14] Kato T., On the Korteweg–deVries equation, Manuscripta Math.28 (1979) 89-99. Zbl0415.35070MR535697
15. [15] Kato T., Masuda K., Nonlinear evolution equations and analyticity I, Ann. Inst. H. Poincaré Anal. Non Linéaire3 (1986) 455-467. Zbl0622.35066MR870865
16. [16] Kato K., Ogawa T., Analyticity and smoothing effect for the Korteweg–de Vries equation with a single point singularity, Math. Ann.316 (2000) 577-608. Zbl0956.35115MR1752786
17. [17] Kenig C.E., Ponce G., Vega L., Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J.40 (1991) 33-69. Zbl0738.35022MR1101221
18. [18] Kenig C.E., Ponce G., Vega L., On the Cauchy problem for the Korteweg–deVries equation in Sobolev spaces of negative indices, Duke Math. J.71 (1993) 1-20. Zbl0787.35090MR1230283
19. [19] Martel Y., Merle F., Blow up in finite time and dynamics of blow up solutions for the $L_2$-critical generalized KdV equation, J. Amer. Math. Soc.15 (2002) 617-664. Zbl0996.35064MR1896235
20. [20] Staffilani G., On the growth of high Sobolev norms of solutions for KdV and Schrödinger equations, Duke Math. J.86 (1997) 109-142. Zbl0874.35114MR1427847

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