Multichannel nonlinear scattering for nonintegrable equations. II: The case of anisotropic potentials and data. (English) Zbl 0795.35073
Summary: The nonlinear scattering and stability results of the authors [Commun. Math. Phys. 133, No. 1, 119-146 (1990; Zbl 0721.35082)] are extended to the case of anisotropic potentials and data. The range of nonlinearities for which the theory is shown to be valid is also extended considerably.
MSC:
| 35P25 | Scattering theory for PDEs |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 81U30 | Dispersion theory, dispersion relations arising in quantum theory |
Keywords:
nonlinear Schrödinger equation; nonlinear scattering and stability theory; anisotropic potentials and dataCitations:
Zbl 0721.35082References:
| [1] | Ginibre, J.; Velo, G., On a class of nonlinear Schrödinger equations I, II, J. Funct. Anal., 32, 1-71 (1979) · Zbl 0396.35029 |
| [3] | Journé, J.-L; Soffer, A.; Sogge, C., Decay estimates for Schrödinger operators, Comm. Pure Appl. Math., 44, 5, 573-604 (1991) · Zbl 0743.35008 |
| [4] | Soffer, A.; Weinstein, M. I., Multichannel nonlinear scattering for nonintegrable equations, Comm. Math. Phys., 133, 119-146 (1990) · Zbl 0721.35082 |
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