Long-time asymptotic behavior of the fifth-order modified KdV equation in low regularity spaces

被引：24

作者：

Liu, Nan ^{[1
]}

Chen, Mingjuan ^{[2
]}

Guo, Boling ^{[3
]}

机构：

[1] Henan Univ, Sch Math & Stat, Kaifeng, Peoples R China

[2] Jinan Univ, Dept Math, Guangzhou 510632, Peoples R China

[3] Inst Appl Phys & Computat Math, Beijing, Peoples R China

来源：

STUDIES IN APPLIED MATHEMATICS | 2021年 / 147卷 / 01期

基金：

中国博士后科学基金;

关键词：

fifth‐ order modified Korteweg– de Vries equation; Fourier analysis; long‐ time asymptotics; low regularity; nonlinear steepest descent method; GLOBAL WELL-POSEDNESS; STEEPEST DESCENT METHOD; INVERSE SCATTERING; MODIFIED KORTEWEG; STABILITY; 1ST;

D O I：

10.1111/sapm.12379

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Based on the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann-Hilbert problems and the Dbar approach, the long-time asymptotic behavior of solutions to the fifth-order modified KdV (Korteweg-de Vries) equation on the line is studied in the case of initial conditions that belong to some weighted Sobolev spaces. Using techniques in Fourier analysis and the idea of the I-method, we give its global well-posedness in lower regularity Sobolev spaces and then obtain the asymptotic behavior in these spaces with weights.

引用

页码：230 / 299

页数：70

共 50 条

[41] Long-time asymptotic for the Hirota equation via nonlinear steepest descent method [J].

Huang, Lin ;

Xu, Jian ;

Fan, En-gui .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2015, 26 :229-262

[42] Long-Time Asymptotics for the Modified Camassa-Holm Equation with Nonzero Boundary Conditions [J].

Karpenko, Iryna .

JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY, 2022, 18 (02) :224-252

[43] ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A HIGHER-ORDER KDV-TYPE EQUATION WITH CRITICAL NONLINEARITY [J].

Okamoto, Mamoru .

EVOLUTION EQUATIONS AND CONTROL THEORY, 2019, 8 (03) :567-601

[44] LONG-TIME SOLVABILITY FOR THE 2D DISPERSIVE SQG EQUATION WITH IMPROVED REGULARITY [J].

Angulo-Castillo, Vladimir ;

Ferreira, Lucas C. F. ;

Kosloff, Leonardo .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (03) :1411-1433

[45] The Interactions of N-Soliton Solutions for the Generalized 2+1-Dimensional Variable-Coefficient Fifth-Order KdV Equation [J].

Wang, Xiangrong ;

Zhang, Xiaoen ;

Zhang, Yong ;

Dong, Huanhe .

ADVANCES IN MATHEMATICAL PHYSICS, 2015, 2015

[46] On the long-time asymptotics of the modified Camassa-Holm equation in space-time solitonic regions [J].

Yang, Yiling ;

Fan, Engui .

ADVANCES IN MATHEMATICS, 2022, 402

[47] LONG-TIME ASYMPTOTIC BEHAVIOR FOR THE GERDJIKOV-IVANOV TYPE OF DERIVATIVE NONLINEAR SCHRODINGER EQUATION WITH TIME-PERIODIC BOUNDARY CONDITION [J].

Tian, Shou-Fu ;

Zhang, Tian-Tian .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (04) :1713-1729

[48] Long-time asymptotics of the good Boussinesq equation with qxx-term and its modified version [J].

Wang, Deng-Shan ;

Zhu, Xiaodong .

JOURNAL OF MATHEMATICAL PHYSICS, 2022, 63 (12)

[49] Long time asymptotic behavior of the focusing nonlinear Schrodinger equation [J].

Borghese, Michael ;

Jenkins, Robert ;

McLaughlin, Kenneth D. T-R .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2018, 35 (04) :887-920

[50] LONG-TIME BEHAVIOR OF SOLUTIONS OF THE GENERALIZED KORTEWEG DE VRIES EQUATION [J].

Said-Houari, Belkacem .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2016, 21 (01) :245-252

← 1 2 3 4 5 →