LARGE TIME ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO HIGHER ORDER NONLINEAR SCHRODINGER EQUATION

被引：0

作者：

Juarez-Campos, Beatriz ^{[1
]}

Naumkin, Pavel, I ^{[2
]}

Ruiz-Paredes, Hector F. ^{[1
]}

机构：

[1] Inst Tecnol Morelia, Ave Tecnol 1500, Morelia 58120, Michoacan, Mexico

[2] Ctr Ciencias Matemat, UNAM Campus Morelia,AP 61-3 Xangari, Morelia 58089, Michoacan, Mexico

来源：

OSAKA JOURNAL OF MATHEMATICS | 2021年 / 58卷 / 03期

关键词：

GLOBAL EXISTENCE; SCATTERING-THEORY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Cauchy problem for the higher-order nonlinear Schrodinger equation (0.1) i partial derivative(t)u + 1/2 partial derivative(2)(x)u = u(3,) t > 0, x is an element of R, u (0, x) = u(0) (x), x is an element of R. The aim of the present paper is prove the global existence of solutions to (0.1) if the initial data u(0) is an element of H-1 boolean AND H-0,H-1. Also we find the large time asymptotics of solutions.

引用

页码：509 / 529

页数：21

共 29 条

[1]

[Anonymous], 1989, ENCY MATH SCI

[2] CLASS OF BOUNDED PSEUDODIFFERENTIAL OPERATORS [J].

CALDERON, AP ;

VAILLANCOURT, R .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1972, 69 (05) :1185-+

[3]

Cazenave T., 2003, COURANT LECT NOTES M

[4] COMPACTNESS OF COMMUTATORS OF MULTIPLICATIONS AND CONVOLUTIONS, AND BOUNDEDNESS OF PSEUDODIFFERENTIAL OPERATORS [J].

CORDES, HO .

JOURNAL OF FUNCTIONAL ANALYSIS, 1975, 18 (02) :115-131

[5] NOTE ON A MODIFICATION TO THE NON-LINEAR SCHRODINGER-EQUATION FOR APPLICATION TO DEEP-WATER WAVES [J].

DYSTHE, KB .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1979, 369 (1736) :105-114

[6]

Fukumoto Y, 2001, FLUID MEC A, V59, P211

[7] Global existence of solutions for a fourth-order nonlinear Schrodinger equation [J].

Guo, Cuihua ;

Cui, Shangbin .

APPLIED MATHEMATICS LETTERS, 2006, 19 (08) :706-711

[8] Wellposedness for the fourth order nonlinear Schrodinger equations [J].

Hao, Chengchun ;

Hsiao, Ling ;

Wang, Baoxiang .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 320 (01) :246-265

[9] GLOBAL EXISTENCE OF SMALL SOLUTIONS TO QUADRATIC NONLINEAR SCHRODINGER-EQUATIONS [J].

HAYASHI, N .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1993, 18 (7-8) :1109-1124

[10]

HAYASHI N, 1988, ANN I H POINCARE-PHY, V48, P17

← 1 2 3 →