A remark on asymptotics of solutions to Schrodinger equation with fourth-order dispersion

被引：5

作者：

Segata, Jun-Ichi ^{[1
]}

机构：

[1] Tohoku Univ, Math Inst, Aoba Ku, Sendai, Miyagi 9808578, Japan

来源：

ASYMPTOTIC ANALYSIS | 2011年 / 75卷 / 1-2期

关键词：

fourth-order Schrodinger type equation; asymptotic behavior; GLOBAL WELL-POSEDNESS; SCATTERING;

D O I：

10.3233/ASY-2011-1051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give an asymptotic formula in time of solutions to the linear fourth-order Schrodinger type equation in one space dimension without the mean zero condition on the initial data. Then we apply this formula to study the long time behavior of solution to the fourth-order Schrodinger type equation with the cubic non-linearity.

引用

页码：25 / 36

页数：12

共 16 条

[1]

[Anonymous], 1993, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals

[2] Dispersion estimates for fourth order Schrodinger equations [J].

Ben-Artzi, M ;

Koch, H ;

Saut, JC .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 330 (02) :87-92

[3] Self-focusing with fourth-order dispersion [J].

Fibich, G ;

Ilan, B ;

Papanicolaou, G .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2002, 62 (04) :1437-1462

[4] Motion and expansion of a viscous vortex ring. Part 1. A higher-order asymptotic formula for the velocity [J].

Fukumoto, Y ;

Moffatt, HK .

JOURNAL OF FLUID MECHANICS, 2000, 417 :1-45

[5] Final state problem for Korteweg-de Vries type equations [J].

Hayashi, Nakao ;

Naumkin, Pavel I. .

JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (12)

[6] Asymptotic properties of solutions to dispersive equation of Schrodinger type [J].

Hayashi, Nakao ;

Naumkin, Pavel I. .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2008, 60 (03) :631-652

[7] Stabilization of soliton instabilities by higher-order dispersion: Fourth-order nonlinear Schrodinger-type equations [J].

Karpman, VI .

PHYSICAL REVIEW E, 1996, 53 (02) :R1336-R1339

[8] OSCILLATORY INTEGRALS AND REGULARITY OF DISPERSIVE EQUATIONS [J].

KENIG, CE ;

PONCE, G ;

VEGA, L .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1991, 40 (01) :33-69

[9]

MIAO C, 2008, GLOBAL WELLPOSEDNESS

[10] Global well-posedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case [J].

Miao, Changxing ;

Xu, Guixiang ;

Zhao, Lifeng .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (09) :3715-3749

← 1 2 →