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

35P25Scattering theory (PDE)
47A10Spectrum and resolvent of linear operators
35Q99PDE of mathematical physics and other areas
35G25Initial value problems for nonlinear higher-order PDE
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35B40Asymptotic behavior of solutions of PDE
Full Text: DOI
[1] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations, preprint. · Zbl 0396.35029
[2] Lin, J. E.: Time decay of two conservative equations. Ph.d. thesis (1976)
[3] Morawetz, C. S.: Notes on time decay and scattering for some hyperbolic problems. (1975) · 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) · Zbl 0276.35066
[6] Reed, M.: Abstract non-linear wave equations. Lecture notes in mathematics no. 507 (1976) · 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, 53-78 (1974)