dinger equations;global solutions;almost global solutions;regularity;"/> dinger equations;global solutions;almost global solutions;regularity;"/> Global Small Solutions of the Cauchy Problem for Nonisotropic Schrödinger Equations | Korea Science
JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Global Small Solutions of the Cauchy Problem for Nonisotropic Schrödinger Equations
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 48, Issue 1,  2008, pp.101-108
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2008.48.1.101
 Title & Authors
Global Small Solutions of the Cauchy Problem for Nonisotropic Schrödinger Equations
Zhao, Xiangqing; Cui, Shangbin;
  PDF(new window)
 Abstract
In this paper we study the existence of global small solutions of the Cauchy problem for the non-isotropically perturbed nonlinear Schrdinger equation:
 Keywords
non-isotropic Schrdinger equations;global solutions;almost global solutions;regularity;
 Language
English
 Cited by
 References
1.
G. Fibich and B. Ilan, Discretization effects in the nonlinear Schrodinger equation, Appl. Numer. Math., 44(2002), 63-75.

2.
S. Wen and D. Fan, Spatiotemporal instabilities in nonlinear kerr media in the presence of arbitrary higher order dispersions, J. Opt. Soc. Am. B, 19(2002), 1653-1659. crossref(new window)

3.
G. Fibich and B. Ilan and S. Schochet, Critical exponents and collapse of nonlinear Schr Odinger equations with anisotropic fourth-order dispersion, Nonliearity, 16(2003), 1809-1821. crossref(new window)

4.
G. Fibich and G. C. Papanicolaou, A modulation method for self-focusing in the perturbed critical nonlinear Schrodinger equation, Phys. Lett. A, 239(1998), 167-173. crossref(new window)

5.
G. Fibich and G. C. Papanicolaou, Self-focusing in the presence of small time dispersion and nonparaxiality, Opti. Lett., 22(1997), 1379-1381. crossref(new window)

6.
F. Ribaud and A. Youssfi, Regular and self-similar solutions of nonlinear Schrodinger equation, J. Math. Pures Appl., 77(1998), 1065-1079. crossref(new window)

7.
Cuihua Guo and Shangbin Cui, Solvability of the Cauchy problem of nonisotropic Schrodinger equation in Sobolev spaces, submitted.

8.
T. Runst and W. Sickel, Sobolev spaces of fractional order, Nemytskii operators and nonlinear partial differential equations, de Gruyter, Berlin, 1996.

9.
S. Cui and S. Tao, Strichartz estimates for dispersive equations and solvability of the Kawahara equation, J. Math. Anal. Appl., 304(2005), 683-702. crossref(new window)

10.
S. Cui, Pointwise estimates for a class of oscillatory integrals and and related $L^{p}-L^{q}$ estimates, J. Fourier Anal. Appl., 11(2005), 441-457. crossref(new window)