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IJMMS
ASYMPTOTIC EXPANSION OF SMALL ANALYTIC SOLUTIONS TO THE QUADRATIC NONLINEAR SCHR?DINGER EQUATIONS IN TWO-DIMENSIONAL SPACES
NAKAO HAYASHI
**PAVEL** **I**. **NAUMKIN**
We study asymptotic behavior in time ... . The works of **Pavel** **I**. **Naumkin** are partially supported by Consejo Nacional
de Ciencia y Tecnologia (CONACYT).
Nakao Hayashi: Department of Mathematics, Graduate School of Science, Osaka
University

IJMMS
ASYMPTOTICS FOR CRITICAL NONCONVECTIVE TYPE EQUATIONS
NAKAO HAYASHI
ELENA I. KAIKINA
**PAVEL** **I**. **NAUMKIN**
We study large-time asymptotic behavior of solutions to the Cauchy problem for a model of ... 1.1 is proved.
Acknowledgments. The work of Elena I. Kaikina and **Pavel** **I**. **Naumkin** is partially
supported by CONACYT. The authors are grateful to the unknown referees for many
useful suggestions and

IJMMS
ASYMPTOTICS FOR CRITICAL NONCONVECTIVE TYPE EQUATIONS
NAKAO HAYASHI
ELENA I. KAIKINA
**PAVEL** **I**. **NAUMKIN**
We study large-time asymptotic behavior of solutions to the Cauchy problem for a model of ... 1.1 is proved.
Acknowledgments. The work of Elena I. Kaikina and **Pavel** **I**. **Naumkin** is partially
supported by CONACYT. The authors are grateful to the unknown referees for many
useful suggestions and

We study the equations governing the high-speed transmission in long-haul electrical systems , , , where , and is the Fourier transformation. Our purpose in this paper is to obtain the large time asymptotics for the solutions under the nonzero mass condition

We study the equations governing the high-speed transmission in long-haul electrical systems , , , where , and is the Fourier transformation. Our purpose in this paper is to obtain the large time asymptotics for the solutions under the nonzero mass condition

.
Acknowledgments
The work of Nakao Hayashi is partially supported by JSPS KAKENHI Grant nos. JP25220702 and JP15H03630. The work of **Pavel** **I**. **Naumkin** is partially supported by CONACYT and PAPIIT Project IN100616

.
Acknowledgments
The work of Nakao Hayashi is partially supported by JSPS KAKENHI Grant nos. JP25220702 and JP15H03630. The work of **Pavel** **I**. **Naumkin** is partially supported by CONACYT and PAPIIT Project IN100616

. 34) and NNSFC
under Grant No. 11461074. The work of **Pavel** **I**. **Naumkin**
is partially supported by CONACYT and PAPIIT Project
IN100113.
[7] N. Okazawa and T. Yokota, ?Global existence and smoothing
effect

Copyright © 2010 Nakao Hayashi and **Pavel** **I**. **Naumkin**. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction

Fernando Bernal-Vlchis
0
Nakao Hayashi
0
**Pavel** **I**. **Naumkin**
0
0
Nakao Hayashi Department of Mathematics, Graduate School of Science, Osaka University
,
Osaka, Tokyonaka
,
Japan
We study the global in ... . 19340030).
**Pavel** **I**. **Naumkin**
e-mail:
Received: 7 May 2010.
Accepted: 6 January 2011.

Nakao Hayashi
0
**Pavel** **I**. **Naumkin**
0
Joel A. Rodriguez-Ceballos
0
0
N. Hayashi Department of Mathematics, Graduate School of Science, Osaka University
, Osaka, Toyonaka 560-0043,
Japan
We study large