Quasi-periodic solutions of nonlinear wave equations with a prescribed potential

被引：19

作者：

Yuan, Xiaoping ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Fudan Univ, Minist Educ, Key Lab Math Nonlinear Sci, Shanghai, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2006年 / 16卷 / 03期

关键词：

nonlinear wave equation; KAM theorem; infinite dimensional Hamiltonian systems; quasi-periodic solutions;

D O I：

10.3934/dcds.2006.16.615

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is proved that for a prescribed potential V there are many quasi-periodic solutions of nonlinear wave equations u(tt) - u(xx) + V(x)u +/- u(3) + O(vertical bar u vertical bar(5)) = subject to Dirichlet boundary conditions.

引用

页码：615 / 634

页数：20

共 50 条

[1] Quasi-periodic solutions of nonlinear wave equations with quasi-periodic forcing
Zhang, Min
Si, Jianguo
[J]. PHYSICA D-NONLINEAR PHENOMENA, 2009, 238 (22) : 2185 - 2215
[2] Quasi-periodic solutions for nonlinear wave equations
Wang, Wei-Min
[J]. COMPTES RENDUS MATHEMATIQUE, 2015, 353 (07) : 601 - 604
[3] Quasi-periodic solutions of completely resonant nonlinear wave equations
Yuan, Xiaoping
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 230 (01) : 213 - 274
[4] Quasi-periodic Solutions for Nonlinear Schrodinger Equations with Legendre Potential
Shi, Guanghua
Yan, Dongfeng
[J]. TAIWANESE JOURNAL OF MATHEMATICS, 2020, 24 (03): : 663 - 679
[5] QUASI-PERIODIC SOLUTIONS OF NONLINEAR BEAM EQUATIONS WITH QUINTIC QUASI-PERIODIC NONLINEARITIES
Tuo, Qiuju
Si, Jianguo
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
[6] Quasi-periodic solutions of derivative nonlinear Schrodinger equations with a given potential
Mi, Lufang
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 390 (01) : 335 - 354
[7] Quasi-periodic solutions for a nonlinear wave equation
Poschel, J
[J]. COMMENTARII MATHEMATICI HELVETICI, 1996, 71 (02) : 269 - 296
[8] Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential
Berti, Massimiliano
Bolle, Philippe
[J]. NONLINEARITY, 2012, 25 (09) : 2579 - 2613
[9] PERIODIC AND QUASI-PERIODIC SOLUTIONS OF NONLINEAR-WAVE EQUATIONS VIA KAM THEORY
WAYNE, CE
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1990, 127 (03) : 479 - 528
[10] Quasi-periodic solutions for nonlinear wave equation with singular Legendre potential
Shi, Guanghua
Yan, Dongfeng
[J]. BOUNDARY VALUE PROBLEMS, 2019, 2019 (1)

← 1 2 3 4 5 →