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Nonlinear scattering theory at low energy. (English) Zbl 0466.47006


MSC:

47A40 Scattering theory of linear operators
35P25 Scattering theory for PDEs
47H20 Semigroups of nonlinear operators
81U05 \(2\)-body potential quantum scattering theory
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[2] Ginibre, J.; Velo, G., On a class of nonlinear Schrödinger equations, I, the Cauchy problem, J. Functional Analysis, 32, 1-32 (1979) · Zbl 0396.35028
[3] Ginibre, J.; Velo, G., On a class of nonlinear Schrödinger equations, II, scattering theory, J. Functional Analysis, 32, 33-71 (1979) · Zbl 0396.35029
[4] Glassey, R. T., On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, J. Math. Phys., 18, 1794-1797 (1977) · Zbl 0372.35009
[6] John, F., Blow-up of solutions of nonlinear wave equations in three dimensions, Manuscripta Math., 28, 235-268 (1979) · Zbl 0406.35042
[10] 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
[11] Reed, M.; Simon, B., (Methods of Modern Mathematical Physics, Vol. III (1979), Academic Press: Academic Press New York), Sect. XI. 13 · Zbl 0405.47007
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[15] Segal, I. E., Space-time decay for solutions of wave equations, Advances in Math., 22, 304-311 (1976) · Zbl 0344.35058
[16] Strauss, W. A., Nonlinear scattering theory, (Scattering Theory in Math. Physics (1974), Reidel: Reidel Dordrecht), 53-78 · Zbl 0297.35062
[17] Strauss, W. A., Dispersion of low-energy waves for two conservative equations, Arch. Rational Mech. Anal., 55, 86-92 (1974) · Zbl 0289.35048
[18] Strauss, W. A., Nonlinear invariant wave equations, (Invariant Wave Equations (Erice 1977). Invariant Wave Equations (Erice 1977), Lecture Notes in Physics No. 78 (1978), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York), 197-249
[19] Strauss, W. A., Everywhere defined wave operators, (Nonlinear Evolution Equations (1978), Academic Press: Academic Press New York), 85-102 · Zbl 0466.47005
[20] Strauss, W. A., Abstract 79T-B77, Amer. Math. Soc. Notices, 26, A274 (1979)
[21] Strichartz, R. S., Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J., 44, 705-714 (1977) · Zbl 0372.35001
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