The Smoothness of Scattering Operators for Sinh-Gordon and Nonlinear Schrödinger Equations

Acta Mathematica Sinica, English Series

Volumn 18, Issue 3, 2002, Pages 549-564

  Wang, Bao Xiang ^a  

^a HEBEI UNIVERSITY   (China)

Author keywords

Nonlinear Schr dinger equation; Sinh Gordon equation; The smoothness of scattering operator

Indexed keywords

EID: 0347935947     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10114-002-0193-7     Document Type: Article

References (26)

1. Nakamura, M., Ozawa, T.: Nonlinear Schrödinger equations in the Sobolev space of critical order. J. Funct. Anal., 155(2), 364-380 (1998)
2. Strauss, W.: Nonlinear Wave Equations, Lecture Notes, AMS, Providence, RI, 73 (1989)
3. Bergh, J.: Löfström J., Interpolation Spaces, Springer-Verlag 1976
4. Triebel, H.: Function Space Theory, Birkhäuser-Verlag (1983)
5. Ozawa, T.: On the critical cases of Sobolev's inequalities. J. Funct. Anal., 127(2), 259-269 (1995)
6. s. Nonlinear Anal. TMA, 14(10), 807-836 (1990)
7. Ginibre, J., Velo, G.: Generalized Strichartz inequalities for the wave equation. J. Funct. Anal., 133(1), 50-68 (1995)
8. Brenner, P.: On scattering and everywhere-defined scattering operators of nonlonear Klein-Gordon equations. J. Diff. Eqns., 56(3), 310-344 (1985)
9. Kapitanskii, L. V.: Weak and yet weak solutions of semilinear wave equations. Comm. Partial Diff. Equations, 19(9-10), 1629-1676 (1994)
10. Wang, B. X.: Bessel (Riesz) potentials on Banach function spaces and their applications I, Theory. Acta Math. Sinica, New Series, 14(3), 327-340 (1998)
11. s, Nonlinear Analysis, TMA, 31(5/6), 573-587 (1998)
12. Ablowitz, M. J., Kaup, D. J., Newell, A. C., Segur H.: Nonlinear evolution equations of physical significance. Phys. Rev. Lett., 31, 125-127 (1973)
13. Brenner, P.: On space-time means and everywhere defined scattering operators for nonlinear Klein-Gordon equations. Math. Z., 186(3), 383-391 (1984)
14. Chern, S. S.: Geometrical interpretation of sinh-Gordon equation. Annals Polinci. Math., 39, 63-69 (1981)
15. Ginibre, J., Velo. G.: Time decay of finite energy solutions of the nonlinear Klein-Gordon and Schrödinger equations. Ann. Inst. H. Poincare. Phys. Theor., 43(4), 399-442 (1985)
16. 1,1. Crelle. Jour., 346, 101-109 (1984)
17. Gu, C. H., Hu, H. S.: On the determination of nonlinear PDE admitting integrable system. Scientia Sinica (Science in China) Series A, 704-719 (1986)
18. Keel, M., Tao, T.: End point Strichartz estimates, Amer. J. of Math., 120(5), 955-980 (1998)
19. Kenig, C. E., Ponce, G., Vega, L.: On the IVP for the nonlinear Schrödinger equations. Contemp. Math., 189, 353-367 (1995)
20. Lindblad, H., Sogge, C. D.: On existence and scattering with minimal regularity for semilinear wave equations, J. of Funct. Anal., 130(2), 357-426 (1995)
21. Morawetz C. S., Strauss W. A.: Decay and scattering of solutions of a nonlinear relativistic wave equation. Comm. Pure Appl. Math., 25, 1-31 (1972)
22. Pecher, H.: Nonlinear small data scattering for the wave and Klein-Gordon equations, Math. Z., 185(2), 261-270 (1984)
23. Pecher, H.: Low energy scattering for nonlinear Klein-Gordon equations. J. of Funct. Anal., 63(1), 101-122 (1985)
24. Strauss, W.: Nonlinear scattering theory at low energy. J. of Funct. Anal., 41(1), 110-133 (1981), 43(3), 281-293 (1981)
25. Strauss, W.: Nonlinear scattering theory at low energy. J. of Funct. Anal., 41(1), 110-133 (1981), 43(3), 281-293 (1981)
26. Bourgain, J.: Global wellposedness of defocusing 3D critical NLS in the radial case. J. Amer. Math. Soc., 12(1), 145-171 (1999)