Asymptotically-free solutions for the short-range nonlinear Schrödinger equation

SIAM Journal on Mathematical Analysis

Volumn 32, Issue 6, 2001, Pages 1265-1271

  Nakanishi, Kenji ^a  

^a KOBE UNIVERSITY   (Japan)

Author keywords

dinger equation; Nonlinear Schr ; Scattering

Indexed keywords

EID: 0035541229     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141000369083     Document Type: Article

References (18)

1. J. E. BARAB, Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation, J. Math. Phys., 25 (1984), pp. 3270-3273.
2. J. BOURGAIN, Refinements of Strichartz' inequality and applications to 2D-NLS with critical nonlinearity, Internat. Math. Res. Notices, 5 (1998), pp. 253-283.
3. J. BOURGAIN, Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case, J. Amer. Math. Soc., 12 (1999), pp. 145-171.
4. T. CAZENAVE AND F. B. WEISSLER, Rapidly decaying solutions of the nonlinear Schrödinger equation, Comm. Math. Phys., 47 (1992), pp. 75-100.
5. J. GINIBRE AND T. OZAWA, Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension n ≥ 2, Comm. Math. Phys., 151 (1993), pp. 619-645.
6. J. GINIBRE, T. OZAWA, AND G. VELO, On the existence of the wave operators for a class of nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor., 60 (1994), pp. 211-239.
7. J. GINIBRE AND G. VELO, On a class of nonliear Schrödinger equations. II. Scattering theory, general case, J. Funct. Anal., 32 (1979), pp. 33-71.
8. J. GINIBRE AND G. VELO, Scattering theory in the energy space for a class of non-linear Schrödinger equations, J. Math. Pures Appl., 64 (1985), pp. 363-401.
9. R. T. GLASSEY, Asymptotic behavior of solutions to certain nonlinear Schrödinger-Hartree equations, Comm. Math. Phys., 53 (1977), pp. 9-18.
10. J. E. LIN AND W. A. STRAUSS, Decay and scattering of solutions of a nonlinear Schrödinger equation, J. Funct. Anal., (1978), pp. 245-263.
11. A. MATSUMURA, On the asymptotic behavior of solutions of semi-linear wave equations, Publ. Res. Inst. Math. Sci., 12 (1976/77), pp. 169-189.
12. K. NAKANISHI, Energy scattering for nonlinear Klein-Gordon and Schrödinger equations in spatial dimensions 1 and 2, J. Funct. Anal., 169 (1999), pp. 201-225.
13. T. OZAWA, Long range scattering for nonlinear Schrödinger equations in one space dimension, Comm. Math. Phys., 139 (1991), pp. 479-493.
14. P. SJÖLIN, Regularity of solutions to the Schrödinger equations, Duke Math. J., 55 (1987), pp. 699-715.
15. W. STRAUSS, Nonlinear Wave Equations, CBMS Reg. Conf. Ser. Math. 73, AMS, Providence, RI, 1989.
16. Y. TSUTSUMI, Scattering problem for nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor., 43 (1985), pp. 321-347.
17. 2-solutions for nonlinear Schrödinger equations and nonlinear groups, Funkcial. Ekvac., 30 (1987), pp. 115-125.
18. Y. TSUTSUMI AND K. YAJIMA, The asymptotic behavior of nonlinear Schrödinger equations, Bull. Amer. Math. Soc. (N.S.), 11 (1984), pp. 186-188.