@article{JEDP_1997____A14_0,
author = {Ponce, Gustavo},
title = {Local existence theory for the generalized Schr\"odinger equation},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
year = {1997},
pages = {1-11},
zbl = {01808672},
language = {en},
url = {http://dml.mathdoc.fr/item/JEDP_1997____A14_0}
}
Ponce, Gustavo. Local existence theory for the generalized Schrödinger equation. Journées équations aux dérivées partielles, (1997), pp. 1-11. http://gdmltest.u-ga.fr/item/JEDP_1997____A14_0/
[AbHa] , and , Nonlinear evolution equations in two and three dimensions, Phys. Rev. Lett. 35 (1975), 1185-1188. | MR 55 #896
[CaVa] , and , A class of bounded pseudodifferential operators, Proc. Nat. Acad. Sci. USA. 69 (1972), 1185-1187. | MR 45 #7532 | Zbl 0244.35074
[Cz] , An introduction to nonlinear Schrödinger equations, Textos de Métodos Matemáticos 22, Universidade Federal do Rio de Janeiro.
[Ch1] , Local existence for semilinear Schrödinger equations, Math. Japonica 42 (1995), 35-52. | MR 96d:35128 | Zbl 0834.35118
[Ch2] , The initial value problem for the elliptic-hyperbolic Davey-Stewartson equation, preprint. | Zbl 0947.35036
[CoSa] , and , Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1989), 413-446. | MR 89d:35150 | Zbl 0667.35061
[CrKaSt] , , and , Microlocal dispersive smoothing for the Schrödinger equation, Comm. Pure Appl. Math. 48 (1995), 769-860. | MR 96m:35057 | Zbl 0856.35106
[DaSe] , and , On three dimensional packets of surface waves, Proc. R. Soc. A 338 (1974), 101-110. | MR 50 #1620 | Zbl 0282.76008
[Do1] , On the Cauchy problem for Schrödinger type equations and the regularity of the solutions, J. Math. Kyoto Univ. 34 (1994), 319-328. | MR 95g:35190 | Zbl 0807.35026
[Do2] , Remarks on the Cauchy problem for Schrödinger type equations, Comm. P.D.E. 21 (1996), 163-178. | MR 96m:35058 | Zbl 0853.35025
[GhSa] , and , On the initial value problem for the Davey-Stewartson systems, Nonlinearity 3 (1990), 475-506. | MR 91h:35299 | Zbl 0727.35111
[Hy1] , Global existence of small analytic solutions to nonlinear Schrödinger equations, Duke Math. J 62 (1991), 575-592. | MR 92f:35127
[Hy2] , Local existence in time of solutions to the elliptic-hyperbolic Davey-Stewartson system without smallness condition on the data, preprint. | Zbl 0907.35120
[HyOz] , and , Remarks on nonlinear Schrödinger equations in one space dimension, Diff. Integral Eqs 2 (1994), 453-461. | MR 94j:35165 | Zbl 0803.35137
[HySa] , and , Global existence of small solutions to the Davey-Stewartson and the Ishimori systems, Diff. Integral Eqs 8 (1995), 1657-1675. | MR 96k:35167 | Zbl 0827.35120
[Is] , Multi vortex solutions of a two dimensional nonlinear wave equation, Progr. Theor. Phys 72 (1984), 33-37. | MR 86c:35139 | Zbl 1074.35573
[Kt] , Quasilinear evolution equation, with applications to partial differential equations, Lecture Notes in Math. 448, 27-50, Springer-Verlag 1975. | MR 53 #11252 | Zbl 0315.35077
[KePoVe1] , , and , Small solutions to nonlinear Schrödinger equations, Annales de l'I.H.P. 10 (1993), 255-288. | Numdam | MR 94h:35238 | Zbl 0786.35121
[KePoVe2] , , and , On the smoothing of some dispersive hyperbolic systems, preprint. | Zbl 0887.35027
[KePoVe3] , , and , On the Cauchy problem for linear Schrödinger systems with variable coefficient lower order terms, preprint. | Zbl 0908.35026
[LiPo] , and , On the Davey-Stewartson systems, Annales de l'I.H.P. Analyse non linéaire 10 (1993), 523-548. | Numdam | MR 94m:35285 | Zbl 0807.35136
[Mi] , On the Cauchy problem, Notes and Reports in Math. in Science and Engineering, Science Press & Academic Press 3 (1985). | MR 89a:35007 | Zbl 0616.35002
[SiTa] , and , Wave operators and analytic solutions for systems of nonlinear Klein-Gordon equations and of non-linear Schrödinger equations, Comm. Math. Phys. 99 (1985), 541-562. | MR 86j:35147 | Zbl 0615.47034
[Sj] , Regularity of solutions to the Schrödinger equations, Duke Math. J. 55 (1987), 699-715. | Zbl 0631.42010
[So] , The Cauchy problem for the Ishimori equations, J. Funct. Anal. 105 (1992), 233-255. | MR 93h:82034 | Zbl 0763.35077
[Tk] , Le problème de Cauchy pour certaines équations aux dérivées partielles du type de Schrödinger, VIII ; symétrisations indépendendantes du temps, C. R. Acad. Sci. Paris t315, Série 1 (1992), 1055-1058. | MR 94a:35031 | Zbl 0768.35066
[Ve] , The Schrödinger equation : pointwise convergence to the initial date, Proc. Amer. Math. Soc. 102 (1988), 874-878. | MR 89d:35046 | Zbl 0654.42014
[ZaSc] , and , Degenerated dispersion laws, motion invariant and kinetic equations, Physica 1D (1980), 185-250. | MR 81j:35077