Compactons and chaos in strongly nonlinear lattices

被引：67

作者：

Ahnert, Karsten ^{[1
]}

Pikovsky, Arkady ^{[1
]}

机构：

[1] Univ Potsdam, Dept Phys & Astron, D-14476 Potsdam, Germany

来源：

PHYSICAL REVIEW E | 2009年 / 79卷 / 02期

关键词：

chaos; lattice theory; nonlinear dynamical systems; solitons; SOLITARY WAVES; CHAIN; DYNAMICS; BEADS;

D O I：

10.1103/PhysRevE.79.026209

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are superexponentially localized and present an accurate numerical method allowing one to find them for an arbitrary nonlinearity index. Compactons evolve from rather general initially localized perturbations and collide nearly elastically. Nevertheless, on a long time scale for finite lattices an extensive chaotic state is generally observed. Because of the system's scaling, these dynamical properties are valid for any energy.

引用

页数：10

共 33 条

[21] Highly nonlinear solitary waves in periodic dimer granular chains [J].

Porter, Mason A. ;

Daraio, Chiara ;

Herbold, Eric B. ;

Szelengowicz, Ivan ;

Kevrekidis, P. G. .

PHYSICAL REVIEW E, 2008, 77 (01)

[22] Pulse velocity in a granular chain [J].

Rosas, A ;

Lindenberg, K .

PHYSICAL REVIEW E, 2004, 69 (03) :037601-1

[23] Pulse dynamics in a chain of granules with friction [J].

Rosas, A ;

Lindenberg, K .

PHYSICAL REVIEW E, 2003, 68 (04) :413041-413041

[24] Hamiltonian dynamics of dense chains and lattices: or how to correct the continuum [J].

Rosenau, P .

PHYSICS LETTERS A, 2003, 311 (01) :39-52

[25] NONLINEAR DISPERSION AND COMPACT STRUCTURES [J].

ROSENAU, P .

PHYSICAL REVIEW LETTERS, 1994, 73 (13) :1737-1741

[26] COMPACTONS - SOLITONS WITH FINITE WAVELENGTH [J].

ROSENAU, P ;

HYMAN, JM .

PHYSICAL REVIEW LETTERS, 1993, 70 (05) :564-567

[27] Solitonlike pulses in perturbed and driven Hertzian chains and their possible applications in detecting buried impurities [J].

Sen, S ;

Manciu, M ;

Wright, JD .

PHYSICAL REVIEW E, 1998, 57 (02) :2386-2397

[28] The quasi-equilibrium phase in nonlinear 1D systems [J].

Sen, S ;

Mohan, TRK ;

Pfannes, JMM .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2004, 342 (1-2) :336-343

[29] Solitary wave dynamics in generalized Hertz chains: An improved solution of the equation of motion [J].

Sen, S ;

Manciu, M .

PHYSICAL REVIEW E, 2001, 64 (05) :4

[30] Sound propagation in impure granular columns [J].

Sen, S ;

Sinkovits, RS .

PHYSICAL REVIEW E, 1996, 54 (06) :6857-6865

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