Multi-Solitary Waves for the Nonlinear Klein-Gordon Equation

被引：21

作者：

Bellazzini, Jacopo ^{[1
]}

Ghimenti, Marco ^{[2
]}

Le Coz, Stefan ^{[3
]}

机构：

[1] Univ Sassari, I-07100 Sassari, Italy

[2] Univ Pisa, Dipartimento Matemat, I-56100 Pisa, Italy

[3] Univ Toulouse 3, Inst Math Toulouse, F-31062 Toulouse 9, France

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 39卷 / 08期

关键词：

Asymptotic behavior; Klein-Gordon equation; Multi-soliton; SCALAR FIELD-EQUATIONS; GLOBAL CAUCHY-PROBLEM; STANDING WAVES; STRONG INSTABILITY; MULTISOLITON SOLUTIONS; ASYMPTOTIC STABILITY; GROUND-STATES; SOLITONS; GKDV; CONSTRUCTION;

D O I：

10.1080/03605302.2013.860988

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the nonlinear Klein-Gordon equation in R-d. We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the composing boosted standing waves are stable. It is obtained by solving the equation backward in time around a sequence of approximate multi-solitary waves and showing convergence to a solution with the desired property. The main ingredients of the proof are finite speed of propagation, variational characterizations of the profiles, modulation theory and energy estimates.

引用

页码：1479 / 1522

页数：44

共 50 条

[41] THE MODULATIONAL INSTABILITY OF THE NONLINEAR KLEIN-GORDON EQUATION
PARKES, EJ
[J]. WAVE MOTION, 1991, 13 (03) : 261 - 275
[42] THE NONRELATIVISTIC LIMIT OF THE NONLINEAR KLEIN-GORDON EQUATION
NAJMAN, B
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1990, 15 (03) : 217 - 228
[43] PERTURBATION THEORY FOR NONLINEAR KLEIN-GORDON EQUATION
刘天贵
颜家壬
[J]. Applied Mathematics and Mechanics(English Edition), 2002, (08) : 987 - 992
[44] Hydrodynamic limits of the nonlinear Klein-Gordon equation
Lin, Chi-Kun
Wu, Kung-Chien
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2012, 98 (03): : 328 - 345
[45] Operational Solution to the Nonlinear Klein-Gordon Equation
G.Bengochea
L.Verde-Star
M.Ortigueira
[J]. Communications in Theoretical Physics, 2018, 69 (05) : 506 - 512
[46] A nonlinear Klein-Gordon equation on Kerr metrics
Nicolas, JP
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2002, 81 (09): : 885 - 914
[47] ORBITAL STABILITY AND SPECTRAL PROPERTIES OF SOLITARY WAVES OF KLEIN-GORDON EQUATION WITH CONCENTRATED NONLINEARITY
Comech, Andrew
Kopylova, Elena
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2021, 20 (06) : 2187 - 2209
[48] WAVEFORM STABILITY ON A NONLINEAR KLEIN-GORDON EQUATION
SCOTT, AC
[J]. PROCEEDINGS OF THE IEEE, 1969, 57 (07) : 1338 - &
[49] Hylomorphic solitons in the nonlinear Klein-Gordon equation
Bellazzini, J.
Benci, V.
Bonanno, C.
Sinibaldi, E.
[J]. DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, 2009, 6 (04) : 311 - 334
[50] NONLINEAR KLEIN-GORDON EQUATION FOR TEMPERED DISTRIBUTIONS
MOTTONI, PD
TESEI, A
[J]. ANNALES DE L INSTITUT HENRI POINCARE SECTION A PHYSIQUE THEORIQUE, 1975, 23 (02): : 137 - 145

← 1 2 3 4 5 →