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Advances in Mathematical Physics
Volume 2016 (2016), Article ID 3702738, 7 pages
http://dx.doi.org/10.1155/2016/3702738
Research Article

Time Decay for Nonlinear Dissipative Schrödinger Equations in Optical Fields

1Department of Mathematics, Graduate School of Science, Osaka University, Osaka, Toyonaka 560-0043, Japan
2Department of Mathematics, College of Science, Yanbian University, No. 977 Gongyuan Road, Yanji, Jilin 133002, China
3Centro de Ciencias Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), 58089 Morelia, MICH, Mexico

Received 11 December 2015; Accepted 18 January 2016

Academic Editor: Yao-Zhong Zhang

Copyright © 2016 Nakao Hayashi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the initial value problem for the nonlinear dissipative Schrödinger equations with a gauge invariant nonlinearity of order for arbitrarily large initial data, where the lower bound is a positive root of for and for Our purpose is to extend the previous results for higher space dimensions concerning -time decay and to improve the lower bound of under the same dissipative condition on : and as in the previous works.