Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation
Annales de l'I.H.P. Physique théorique, Volume 68 (1998) no. 2, pp. 159-177.
@article{AIHPA_1998__68_2_159_0,
     author = {Hayashi, Nakao and Naumkin, Pavel I.},
     title = {Asymptotic behavior in time of solutions to the derivative nonlinear {Schr\"odinger} equation},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {159--177},
     publisher = {Gauthier-Villars},
     volume = {68},
     number = {2},
     year = {1998},
     mrnumber = {1618664},
     zbl = {0934.35163},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1998__68_2_159_0/}
}
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Hayashi, Nakao; Naumkin, Pavel I. Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation. Annales de l'I.H.P. Physique théorique, Volume 68 (1998) no. 2, pp. 159-177. http://archive.numdam.org/item/AIHPA_1998__68_2_159_0/

[1] A. Friedman, Partial Differential Equations, New York, Holt-Rinehart and Winston, 1969. | MR | Zbl

[2] T. Cazenave, Equation de Schrödinger non lineairés en dimension deau, Proceeding of the Royal Society of Edinburgh, Vol. 84 A, 1979, pp. 327-346. | MR | Zbl

[3] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case; II Scattering theory, general case, J. Funct. Anal., Vol. 32, 1979, pp. 1-71. | MR | Zbl

[4] J. Ginibre and T. Ozawa, Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension n ≥ 2, Commun. Math. Phys., Vol. 151, 1993, pp. 619-645. | MR | Zbl

[5] J. Ginibre, T. Ozawa and G. Velo, On the existence of wave operators for a class of nonlinear Schrödinger equations, Ann. IHP (Phys. Théor), Vol. 60, 1994, pp. 211-239. | Numdam | MR | Zbl

[6] N. Hayashi, The initial value problem for the derivative nonlinear Schrödinger equation in the energy space, J. Nonlinear Anal. T.M.A., Vol. 32, 1993, pp. 823-833. | MR | Zbl

[7] N. Hayashi and T. Ozawa, On the derivative nonlinear Schrödinger equation, Physica D, Vol. 55, 1992, pp. 14-36. | MR | Zbl

[8] N. Hayashi and T. Ozawa, Finite energy solutions of nonlinear Schrödinger equations of derivative type, SIAM J. Math. Anal., Vol. 25, 1994, pp. 1488-1503. | MR | Zbl

[9] N. Hayashi and T. Ozawa, Modified wave operators for the derivative nonlinear Schödinger equations, Math. Annalen, Vol. 298, 1994, pp. 557-576. | MR | Zbl

[10] N. Hayashi and M. Tsutsumi, L∞-decay of classical solutions for nonlinear Schrödinger equations, Proceeding of the Royal Society of Edinburgh, Vol. 104A, 1986, pp. 309-327. | MR | Zbl

[11] N. Hayashi and Y. Tsutsumi, Remarks on the scattering problem for nonlinear Schrödinger equations, Differential Equations and Mathematical Physics, Lecture Note in Mathematics, Edited by I.W. Knowles and Y. Saito, Springer-Verlag, Vol. 1285, 1986, pp. 162-168. | MR | Zbl

[12] N. Hayashi, K. Nakamitsu and M. Tsutsumi, On solutions of the initial value problem for the nonlinear Schrödinger equations in one space dimension, Math. Z., Vol. 192, 1986, pp. 637-650. | MR | Zbl

[13] N. Hayashi, K. Nakamitsu and M. Tsutsumi, On solutions of the initial value problem for nonlinear Schrödinger equations, J. Funct. Anal., Vol. 71, 1987, pp. 218-245. | MR | Zbl

[14] N. Hayashi and P.I. Naumkin, Large time asymptotics of solutions to the generalized Benjamin-Ono equation, Trans. A.M.S. (to appear). | MR | Zbl

[15] S. Katayama and Y. Tsutsumi, Global existence of solutions for nonlinear Schrödinger equations in one space dimension, Commun. P.D.E., Vol. 19, 1994, pp. 1971-1997. | MR | Zbl

[16] D.J. Kaup and A.C. Newell, An exact solution for a derivative nonlinear Schrödinger equation, J. Math. Phys., Vol. 19, 1978, pp. 789-801. | MR | Zbl

[17] A. Kundu, Landau-Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger type equations, J. Math. Phys., Vol. 25, 1984, pp. 3433-3438. | MR

[18] W. Mio, T. Ogino, K. Minami and S. Takeda, Modified nonlinear Schrödinger equation for Alfven waves propagating along the magnetic field in cold plasmas, J. Phys. Soc. Japan, Vol. 41, pp. 265-271. | MR

[19] E. Mjølhus, On the modulational instability of hydromagnetic waves parallel to the magnetic field, J. Plasma Phys., Vol. 16, 1976, pp. 321-334.

[20] P.I. Naumkin, Asymptotics for large time for nonlinear Schrödinger equation, The Proceedings of the 4th MSJ International Reserch Institute on "Nonlinear Waves", GAKUTO International Series, Mathematical Sciences and Applications, Gakkotosho, 1996 (to appear). | MR | Zbl

[21] P.I. Naumkin, Asymptotics for large time of solutions to nonlinear Schrödinger equations (in Russian), Izvestia RAS, ser. Math. (to appear).

[22] T. Ozawa, Long range scattering for nonlinear Schrödinger equations in one space dimension, Commun. Math. Phys., Vol. 139, 1991, pp. 479-493. | MR | Zbl

[23] M. Tsutsumi and I. Fukuda, On solutions of the derivative nonlinear Schrödinger equation. Existence and uniqueness theorem, Funkcialaj Ekvacioj, Vol. 23, 1981, pp. 259-277. | MR | Zbl

[24] M. Tsutsumi and I. Fukuda, On solutions of the derivative nonlinear Schrödinger equation II, Funkcialaj Ekvacioj, Vol. 24, 1981, pp. 85-94. | MR | Zbl

[25] Y. Tsutsumi, Scattering problem for nonlinear Schrödinger equations, Ann. IHP (Phys. Théor.), Vol. 43, 1985, pp. 321-347. | Numdam | MR | Zbl