References
Barab, J.E.: Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation. J. Math. Phys.25, 3270–3273 (1984)
Cazenave, T., Weissler, F.B.: The Cauchy problem for the critical nonlinear Schrödinger equation inH s. Nonlinear Anal., Theory Methods Appl.14, 807–836 (1990)
Flato, M., Simon, J., Taflin, E.: On global solutions of the Maxwell-Dirac equations. Commun. Math. Phys.112, 21–49 (1987)
Ginibre, J.: Unpublished, untitled note
Hayashi, N.: The initial value problem for the derivative nonlinear Schrödinger equation in the energy space. Nonlinear Anal., Theory Methods Appl.32, 823–833 (1993)
Hayashi, N., Ozawa, T.: On the derivative nonlinear Schjrödinger equation. Physica D55, 14–36 (1992)
Hayashi, N., Ozawa, T.: Finite energy solutions of nonlinear Schrödinger equations of derivative type. Hokkaido Univ. Preprint Ser. Math.191 (1993), to appear in SIAM J. Math. Anal.
Kato, T.: On nonlinear Schrödinger equations. Ann. Inst. Henri Poincaré, Phys. Théor.46, 113–129 (1987)
Mio, W., Ogino, T., Minami, K., Takeda, S.: Modified nonlinear Schrödinger equation for Alfven waves propagating along the magnetic field in cold plasmas. J. Phys. Soc. Japan41, 265–271 (1976)
Mjølhus, E.: On the modulational instability of hydromagnetic waves parallel to the magnetic field. J. Plasma Phys.16, 321–334 (1976)
Ozawa, T.: Long range scattering for nonlinear Schrödinger equations in one space dimension. Commun. Math. Phys.139, 479–493 (1991)
Ozawa, T., Tsutsumi, Y.: Global existence and asymptotic behavior of solutions for the Zakharov equations in three space dimensions. Hokkaido Univ. Preprint Ser. Math.195 (1993)
Strauss, W.A.: Nonlinear scattering theory. In: Lavita, J.A., Marchand, J.P. (eds.) Scattering theory in mathematical physics, pp. 53–78. Dordrecht: Reidel 1974
Tsutsumi, Y.: Global existence and asymptotic behavior of solutions for nonlinear Schrödinger equations. Doctoral Thesis. University of Tokyo 1985
Tsutsumi, Y.: Global existence and asymptotic behavior of solutions for the Maxwell-Schrödinger equations in three space dimensions. Commun. Math. Phys.151, 543–576 (1993)
Yajima, K.: Existence of solutions for Schrödinger evolution equations. Commun. Math. Phys.110, 415–426 (1987)
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Dedicated to Professor Hiroki Tanabe on his sixtieth birthday
Partially supported by Grant-in-Aid for Scientific Research, Ministry of Education, Science and Culture
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Hayashi, N., Ozawa, T. Modified wave operators for the derivative nonlinear Schrödinger equation. Math. Ann. 298, 557–576 (1994). https://doi.org/10.1007/BF01459751
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DOI: https://doi.org/10.1007/BF01459751