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 53 条

[41]

Ohta M, 2005, DISCRETE CONT DYN S, V12, P315

[42] Strong instability of standing waves for the nonlinear Klein-Gordon equation and the Klein-Gordon-Zakharov system [J].