The derivative nonlinear schrödinger equation in analytic classes

Journal of Nonlinear Mathematical Physics

Volumn 10, Issue , 2003, Pages 62-71

  Grujić, Zoran ^a   Kalisch, Henrik ^b  

^a UNIVERSITY OF VIRGINIA   (United States)

^b LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746634286     PISSN: 14029251     EISSN: 17760852     Source Type: Journal    
DOI: 10.2991/jnmp.2003.10.s1.5     Document Type: Article

References (24)

1. Bona, J L, and Grujić, Z. 2003. Spatial Analyticity Properties for Nonlinear Waves. Math. Models and Methods in Appl. Sciences, 13:345–360.
2. Bourgain, J. 1993. Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations. GAFA, 3:107–156. 209–262
3. Bourgain, J, and Colliander, J. 1996. On Wellposedness of the Zakharov System. Internat. Math. Res. Notices,:515–546.
4. Colliander, J, Keel, M, Staffilani, G, Takaoka, H, and Tao, T. 2001. Global Well-Posedness for KdV in Sobolev Spaces of Negative Index. Electron. J. Diff. Eq.,:1–7.
5. 2. Math. Res. Lett., 6:755–778.
6. Foias, C, and Temam, R. 1989. Gevrey Class Regularity for the Solutions of the Navier–Stokes Equations. J. Funct. Anal., 87:359–369.
7. Ginibre, J, Tsutsumi, Y, and Velo, G. 1997. On the Cauchy Problem for the Zakharov System. J. Funct. Anal., 151:384–436.
8. Grujić, Z, and Kalisch, H. 2002. Local Well-Posedness of the Generalized Korteweg-de Vries Equation in Spaces of Analytic Functions. Diff. Int. Eq., 15:1325–1334.
9. Hayashi, N. 1991. Analyticity of Solutions of the Korteweg-de Vries Equation. SIAM J. Math. Anal., 22:1738–1743.
10. Hayashi, N. 1991. Solutions of the (Generalized) Korteweg-de Vries Equation in the Bergman and Szegö Spaces on a Sector. Duke Math. J., 62:575–591.
11. Hayashi, N. 1990. Global Existence of Small Analytic Solutions to Nonlinear Schrödinger Equations. Duke Math. J., 60:717–727.
12. Hayashi, N. 1993. The Initial Value Problem for the Derivative Nonlinear Schrödinger Equation in the Energy Space. Nonlin. Anal., 20:823–833.
13. Hayashi, N, and Ozawa, T. 1994. Finite Energy Solutions of Nonlinear Schrödinger Equations of Derivative Type. SIAM J. Math. Anal., 25:1488–1503.
14. Hayashi, N, and Ozawa, T. 1992. On the Derivative Nonlinear Schrödinger Equation. Phys., D55:14–36.
15. Hayashi, N, and Ozawa, T. 1994. Remarks on Nonlinear Schrödinger Equations in One Space Dimension. Diff. Int. Eq., 7:453–461.
16. Kato, T, and Masuda, K. 1986. Nonlinear Evolution Equations and Analyticity I. Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 3:455–467.
17. Kenig, C E, Ponce, G, and Vega, L. 1993. On the Cauchy Problem for the Korteweg-deVries Equation in Sobolev Spaces of Negative Indices. Duke Math. J., 71:1–20.
18. Kenig, C E, Ponce, G, and Vega, L. 1996. A Bilinear Estimate with Applications to the KdV Equation. J. Am. Math. Soc., 9:573–603.
19. Kenig, C E, Ponce, G, and Vega, L. 1996. Quadratic Forms for the 1-D Semilinear Schrödinger Equation. Trans. Amer. Math. Soc., 348:3323–3353.
20. Kenig, C E, Ponce, G, and Vega, L. 1991. Oscillatory Integrals and Regularity of Dispersive Equations. Indiana Univ. Math. J., 40:33–69.
21. Kenig, C E, and Ruiz, A. 1983. A Strong Type (2, 2) Estimate for a Maximal Operator Associated to the Schrödinger Equation. Trans. Amer. Math. Soc., 280:239–246.
22. Takaoka, H. 1999. Well-Posedness for the One-Dimensional Nonlinear Schrödinger Equation with the Derivative Nonlinearity. Adv. Diff. Eq., 4:561–580.
23. Takaoka, H. 2000. Well-Posedness for the Higher Order Nonlinear Schrödinger Equation. Adv. Math. Sci. Appl., 10:149–171.
24. Takaoka, H. 2001. Global Well-Posedness for Schrödinger Equations with Derivative in a Nonlinear Term and Data in Low-Order Sobolev Spaces. Electron. J. Diff. Eq.,:1–23.