Solitary waves for nonconvex FPU lattices

被引：22

作者：

Schwetlick, Hartmut ^{[1
]}

Zimmer, Johannes ^{[1
]}

机构：

[1] Univ Bath, Bath BA2 7AY, Avon, England

来源：

JOURNAL OF NONLINEAR SCIENCE | 2007年 / 17卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

discrete nonlinear elasticity; nonconvex energy; lattice dynamics; solitary waves; double well; STRESS-STRAIN RELATIONS; PHASE-TRANSITIONS; TRAVELING-WAVES; EXISTENCE; DYNAMICS; CHAINS;

D O I：

10.1007/s00332-005-0735-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Solitary waves in a one-dimensional chain of atoms {q(j)}(j is an element of Z) are investigated. The potential energy is required to be monotone and grow super-quadratically. The existence of solitary waves with a prescribed asymptotic strain is shown under certain assumptions on the asymptotic strain and the wave speed. It is demonstrated that the invariance of the equations allows one to transform a system with nonconvex potential energy density to the situation under consideration.

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页码：1 / 12

页数：12

相关论文

共 18 条

[1] KINETIC RELATIONS AND THE PROPAGATION OF PHASE BOUNDARIES IN SOLIDS [J].

ABEYARATNE, R ;

KNOWLES, JK .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1991, 114 (02) :119-154

[2] Two novel methods and multi-mode periodic solutions for the Fermi-Pasta-Ulam model [J].

Arioli, G ;

Koch, H ;

Terracini, S .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2005, 255 (01) :1-19

[3] Dynamics of chains with non-monotone stress-strain relations. I. Model and numerical experiments [J].

Balk, AM ;

Cherkaev, AV ;

Slepyan, LI .

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2001, 49 (01) :131-148

[4] Dynamics of chains with non-monotone stress-strain relations. II. Nonlinear waves and waves of phase transition [J].

Balk, AM ;

Cherkaev, AV ;

Slepyan, LI .

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2001, 49 (01) :149-171

[5] FINE PHASE MIXTURES AS MINIMIZERS OF ENERGY [J].

BALL, JM ;

JAMES, RD .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1987, 100 (01) :13-52

[6]

FERMI E, 1974, LECT APPL MATH, V15

[7] Solitary waves on FPU lattices: I. Qualitative properties, renormalization and continuum limit [J].

Friesecke, G ;

Pego, RL .

NONLINEARITY, 1999, 12 (06) :1601-1627

[8] EXISTENCE THEOREM FOR SOLITARY WAVES ON LATTICES [J].

FRIESECKE, G ;

WATTIS, JAD .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 161 (02) :391-418

[9] Implicit time discretization and global existence for a quasi-linear evolution equation with nonconvex energy [J].

Friesecke, G ;

Dolzmann, G .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1997, 28 (02) :363-380

[10] Travelling waves in a chain of coupled nonlinear oscillators [J].

Iooss, G ;

Kirchgässner, K .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 211 (02) :439-464