Stability of standing waves for a nonlinear Klein-Gordon equation with delta potentials

被引：4

作者：

Csobo, Elek ^{[1
]}

Genoud, Francois ^{[2
]}

Ohta, Masahito ^{[3
]}

Royer, Julien ^{[4
]}

机构：

[1] Delft Univ Technol, Van Mourik Broekmanweg 6, NL-2628 XE Delft, Netherlands

[2] Ecole Polytech Fed Lausanne, Stn 4, CH-1015 Lausanne, Switzerland

[3] Tokyo Univ Sci, Shinjuku Ku, 1-3 Kagurazaka, Tokyo 1628601, Japan

[4] Univ Toulouse 3, Inst Math Toulouse, 118 Route Narbonne, F-31062 Toulouse 9, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2019年 / 268卷 / 01期

关键词：

Nonlinear Klein-Gordon equation; Standing waves; Orbital stability; Delta potential; SCHRODINGER-EQUATION; SOLITARY WAVES; STRONG INSTABILITY; ORBITAL STABILITY; SOLITONS;

D O I：

10.1016/j.jde.2019.08.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point argument. Unlike the unperturbed case, a noteworthy difficulty here arises from the possible non-unitarity of the semigroup generating the corresponding linear evolution. We then show that the equation is Hamiltonian and we establish several stability/instability results for its standing waves. Our analysis relies on a detailed study of the spectral properties of the linearization of the equation, and on the well-known 'slope condition' for orbital stability. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：353 / 388

页数：36

共 32 条

[1] Stability and Symmetry-Breaking Bifurcation for the Ground States of a NLS with a δ′ Interaction [J].