Local existence theory for the generalized Schrödinger equation
Journées équations aux dérivées partielles (1997), article no. 14, 11 p. 
@incollection{JEDP_1997____A14_0,
     author = {Ponce, Gustavo},
     title = {Local existence theory for the generalized {Schr\"odinger} equation},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {14},
     pages = {1--11},
     publisher = {Ecole polytechnique},
     year = {1997},
     zbl = {01808672},
     language = {en},
     url = {http://archive.numdam.org/item/JEDP_1997____A14_0/}
}
TY  - JOUR
AU  - Ponce, Gustavo
TI  - Local existence theory for the generalized Schrödinger equation
JO  - Journées équations aux dérivées partielles
PY  - 1997
SP  - 1
EP  - 11
PB  - Ecole polytechnique
UR  - http://archive.numdam.org/item/JEDP_1997____A14_0/
LA  - en
ID  - JEDP_1997____A14_0
ER  - 
%0 Journal Article
%A Ponce, Gustavo
%T Local existence theory for the generalized Schrödinger equation
%J Journées équations aux dérivées partielles
%D 1997
%P 1-11
%I Ecole polytechnique
%U http://archive.numdam.org/item/JEDP_1997____A14_0/
%G en
%F JEDP_1997____A14_0
Ponce, Gustavo. Local existence theory for the generalized Schrödinger equation. Journées équations aux dérivées partielles (1997), article  no. 14, 11 p. http://archive.numdam.org/item/JEDP_1997____A14_0/

[AbHa] Ablowitz, M. J., and Haberman, R., Nonlinear evolution equations in two and three dimensions, Phys. Rev. Lett. 35 (1975), 1185-1188. | MR

[CaVa] Calderón, A. P., and Vaillancourt, R., A class of bounded pseudodifferential operators, Proc. Nat. Acad. Sci. USA. 69 (1972), 1185-1187. | MR | Zbl

[Cz] Cazenave, T., An introduction to nonlinear Schrödinger equations, Textos de Métodos Matemáticos 22, Universidade Federal do Rio de Janeiro.

[Ch1] Chihara, H., Local existence for semilinear Schrödinger equations, Math. Japonica 42 (1995), 35-52. | MR | Zbl

[Ch2] Chihara, H., The initial value problem for the elliptic-hyperbolic Davey-Stewartson equation, preprint. | Zbl

[CoSa] Constantin, P., and Saut, J. C., Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1989), 413-446. | MR | Zbl

[CrKaSt] Craig, W., Kappeler T., and Strauss, W., Microlocal dispersive smoothing for the Schrödinger equation, Comm. Pure Appl. Math. 48 (1995), 769-860. | MR | Zbl

[DaSe] Davey, A., and Stewartson, K., On three dimensional packets of surface waves, Proc. R. Soc. A 338 (1974), 101-110. | MR | Zbl

[Do1] Doi, S., On the Cauchy problem for Schrödinger type equations and the regularity of the solutions, J. Math. Kyoto Univ. 34 (1994), 319-328. | MR | Zbl

[Do2] Doi, S., Remarks on the Cauchy problem for Schrödinger type equations, Comm. P.D.E. 21 (1996), 163-178. | MR | Zbl

[GhSa] Ghidaglia, J. M., and Saut, J. C., On the initial value problem for the Davey-Stewartson systems, Nonlinearity 3 (1990), 475-506. | MR | Zbl

[Hy1] Hayashi, N., Global existence of small analytic solutions to nonlinear Schrödinger equations, Duke Math. J 62 (1991), 575-592. | MR

[Hy2] Hayashi, N., Local existence in time of solutions to the elliptic-hyperbolic Davey-Stewartson system without smallness condition on the data, preprint. | Zbl

[HyOz] Hayashi, N., and Ozawa, T., Remarks on nonlinear Schrödinger equations in one space dimension, Diff. Integral Eqs 2 (1994), 453-461. | MR | Zbl

[HySa] Hayashi, N., and Saut, J.-C., Global existence of small solutions to the Davey-Stewartson and the Ishimori systems, Diff. Integral Eqs 8 (1995), 1657-1675. | MR | Zbl

[Is] Ishimori, Y., Multi vortex solutions of a two dimensional nonlinear wave equation, Progr. Theor. Phys 72 (1984), 33-37. | MR | Zbl

[Kt] Kato, T., Quasilinear evolution equation, with applications to partial differential equations, Lecture Notes in Math. 448, 27-50, Springer-Verlag 1975. | MR | Zbl

[KePoVe1] Kenig, C. E., Ponce, G., and Vega, L., Small solutions to nonlinear Schrödinger equations, Annales de l'I.H.P. 10 (1993), 255-288. | Numdam | MR | Zbl

[KePoVe2] Kenig, C. E., Ponce, G., and Vega, L., On the smoothing of some dispersive hyperbolic systems, preprint. | Zbl

[KePoVe3] Kenig, C. E., Ponce, G., and Vega, L., On the Cauchy problem for linear Schrödinger systems with variable coefficient lower order terms, preprint. | Zbl

[LiPo] Linares, F., and Ponce, G., On the Davey-Stewartson systems, Annales de l'I.H.P. Analyse non linéaire 10 (1993), 523-548. | Numdam | MR | Zbl

[Mi] Mizohata, S., On the Cauchy problem, Notes and Reports in Math. in Science and Engineering, Science Press & Academic Press 3 (1985). | MR | Zbl

[SiTa] Simon, J., and Taflin, E., 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 | Zbl

[Sj] Sjölin, P., Regularity of solutions to the Schrödinger equations, Duke Math. J. 55 (1987), 699-715. | Zbl

[So] Souyer, A., The Cauchy problem for the Ishimori equations, J. Funct. Anal. 105 (1992), 233-255. | MR | Zbl

[Tk] Takeuchi, J., 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 | Zbl

[Ve] Vega, L., The Schrödinger equation : pointwise convergence to the initial date, Proc. Amer. Math. Soc. 102 (1988), 874-878. | MR | Zbl

[ZaSc] Zakharov, V. E., and Schulman, E. I., Degenerated dispersion laws, motion invariant and kinetic equations, Physica 1D (1980), 185-250. | MR