On the solitary wave pulse in a chain of beads

被引：59
作者：
English, JM [1 ]
Pego, RL
机构：
[1] Univ Wisconsin, Dept Math, Madison, WI 53705 USA
[2] Univ Maryland, Dept Math, College Pk, MD 20742 USA
[3] Univ Maryland, Inst Phys Sci & Technol, College Pk, MD 20742 USA
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 133卷 / 06期
关键词：
solitons; lattice; differential-difference equations; wave propagation;
D O I：
10.1090/S0002-9939-05-07851-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the shape of solitary wave pulses that propagate in an infinite chain of beads initially in contact with no compression. For this system, the repulsive force between two adjacent beads is proportional to the p(th) power of the distance of approach of their centers with p = 3/2. It is known that solitary wave solutions exist for such a system when p > 1. We prove extremely fast, double-exponential, asymptotic decay for these wave pulses. An iterative method of solution is also proposed and is seen to work well numerically.
引用
收藏
页码：1763 / 1768
页数：6
相关论文
共 7 条
[1]   SOLITARY-WAVE SOLUTIONS OF NONLINEAR PROBLEMS [J].
BENJAMIN, TB ;
BONA, JL ;
BOSE, DK .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1990, 331 (1617) :195-244
[2]   Asymptotic solution for solitary waves in a chain of elastic spheres [J].
Chatterjee, A .
PHYSICAL REVIEW E, 1999, 59 (05) :5912-5919
[3]   Solitary waves in a chain of beads under Hertz contact [J].
Coste, C ;
Falcon, E ;
Fauve, S .
PHYSICAL REVIEW E, 1997, 56 (05) :6104-6117
[4]   Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit [J].
Friesecke, G ;
Pego, RL .
NONLINEARITY, 1999, 12 (06) :1601-1627
[5]   EXISTENCE THEOREM FOR SOLITARY WAVES ON LATTICES [J].
FRIESECKE, G ;
WATTIS, JAD .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 161 (02) :391-418
[6]   Existence criterion of solitary waves in a chain of grains [J].
Ji, JY ;
Hong, JB .
PHYSICS LETTERS A, 1999, 260 (1-2) :60-61
[7]   Solitary waves in a chain of beads under Hertz contact [J].
MacKay, RS .
PHYSICS LETTERS A, 1999, 251 (03) :191-192
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