QUASI-PERIODIC SOLUTIONS FOR NON-AUTONOMOUS MKDV EQUATION

被引：1

作者：

Cui, Wenyan ^{[1
]}

Mi, Lufang ^{[1
]}

Yin, Li ^{[1
]}

机构：

[1] Binzhou Univ, Coll Sci, Binzhou, Peoples R China

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2018年 / 49卷 / 02期

关键词：

Quasi-periodic solution; non-autonomous mKdV equation; KAM theory; normal form; DE-VRIES EQUATION; SCHRODINGER-OPERATORS; KAM; CONVERGENCE; SCHEME;

D O I：

10.1007/s13226-018-0271-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the non-autonomous modified Korteweg-de Vries (mKdV) equation u(t) = u(xxx) - 6f(omega t)u(2)u(x), x is an element of R/2 pi Z, where f (omega t) is real analytic and quasi-periodic in t with frequency vector omega = (omega(1), omega(2),...,omega(m)). Basing on an abstract infinite dimensional KAM theorem dealing with unbounded perturbation vector-field, we obtain the existence of Cantor families of smooth quasi-periodic solutions.

引用

页码：313 / 337

页数：25

共 37 条

[1]

Ablowitz M. J., 1981, SIAM Studies in Applied Mathematics, V4, DOI 10.1137/1.9781611970883

[2]

Ablowitz M.J., 1991, Nonlinear Evolution Equations and Inverse Scattering

[3] Time quasi-periodic unbounded perturbations of Schrodinger operators and KAM methods [J].

Bambusi, D ;

Graffi, S .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 219 (02) :465-480

[4] Quasi-periodic solutions of completely resonant forced wave equations [J].

Berti, M ;

Procesi, M .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2006, 31 (06) :959-985

[5] Recent progress on quasi-periodic lattice Schrodinger operators and Hamiltonian PDEs [J].

Bourgain, J .

RUSSIAN MATHEMATICAL SURVEYS, 2004, 59 (02) :231-246

[6] The generalized Korteweg-de Vries equation on the half line [J].

Colliander, JE ;

Kenig, CE .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2002, 27 (11-12) :2187-2266

[7] CONVERGENCE OF A HIGHER ORDER SCHEME FOR THE KORTEWEG-DE VRIES EQUATION [J].

Dutta, Rajib ;

Koley, Ujjwal ;

Risebro, Nils Henrik .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2015, 53 (04) :1963-1983

[8] KORTEWEG-DE VRIES EQUATION AND GENERALIZATIONS .4. KORTEWEG-DE VRIES EQUATION AS A HAMILTONIAN SYSTEM [J].

GARDNER, CS .

JOURNAL OF MATHEMATICAL PHYSICS, 1971, 12 (08) :1548-&

[9] Convergence of a fully discrete finite difference scheme for the Korteweg-de Vries equation [J].

Holden, Helge ;

Koley, Ujjwal ;

Risebro, Nils Henrik .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2015, 35 (03) :1047-1077

[10] THE CONSTRUCTION OF QUASI-PERIODIC SOLUTIONS OF QUASI-PERIODIC FORCED SCHRODINGER EQUATION [J].

Jiao, Lei ;

Wang, Yiqian .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (05) :1585-1606

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