Decay and scattering of solutions of a nonlinear Schrödinger equation. (English) Zbl 0395.35070


35P25 Scattering theory for PDEs
47A10 Spectrum, resolvent
35Q99 Partial differential equations of mathematical physics and other areas of application
35G25 Initial value problems for nonlinear higher-order PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
Full Text: DOI


[1] J. Ginibre and G. Velo; J. Ginibre and G. Velo · Zbl 0396.35029
[2] Lin, J. E., Time Decay of Two Conservative Equations, (Ph.D. thesis (1976), Brown University)
[3] Morawetz, C. S., Notes on time decay and scattering for some hyperbolic problems (1975), SIAM · Zbl 0303.35002
[4] 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) · Zbl 0228.35055
[5] Pecher, H., Das Verhalten globaler Lösungen nichtlinearer Wellengleichungen für grosse Zeiten, (Doctoral Thesis (1974), Göttingen University) · Zbl 0265.35051
[6] Reed, M., Abstract Non-linear Wave Equations, (Lecture Notes in Mathematics No. 507 (1976), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York) · Zbl 0317.35002
[7] Segal, I. E., Nonlinear semigroups, Ann. of Math., 78, 339-364 (1963)
[8] Strauss, W. A., On weak solutions of semi-linear hyperbolic equations, An. Acad. Brasil Ci., 42, 645-651 (1970) · Zbl 0217.13104
[9] Strauss, W. A., Nonlinear scattering theory, (Scattering Theory in Mathematical Physics (1974), Reidel: Reidel Dordrecht), 53-78 · Zbl 0297.35062
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