Being stable and discrete

被引:28
作者
Balmforth, NJ
Craster, RV [1 ]
Kevrekidis, PG
机构
[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2BZ, England
[2] CNR, Ist Cosmogeofis, I-10133 Turin, Italy
[3] Rutgers State Univ, Dept Phys & Astron, Piscataway, NJ 08855 USA
来源
PHYSICA D | 2000年 / 135卷 / 3-4期
基金
英国工程与自然科学研究理事会;
关键词
discretization; sine-Gordon equation; Evans function; localized objects;
D O I
10.1016/S0167-2789(99)00137-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Many discrete lattice systems possess solutions that take the form of localized, stationary structures. In this communication we introduce the discrete version of the Evans function, an analytic function whose zeros correspond to the eigenvalues of the linear stability problem for a spatially localized equilibrium solution. This function provides a convenient and useful tool for investigating the linear eigenvalue spectrum, Notably, it allow's us to construct sufficient stability conditions and detect "internal modes" (neutral oscillatory modes that correspond to localized oscillations about the static structure). We illustrate with the discrete sine-Gordon equation, also known as the Frenkel-Kontorova model. A complementary approach suitable for systems with nearest neighbour coupling and based upon techniques of linear algebra (the bisection method) is also described. (C)2000 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:212 / 232
页数:21
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