Interacting solitary waves in a damped driven Lennard-Jones chain

Theo P. Valkering, Joost H.J. van Opheusden

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Abstract

It is shown analytically that pulse solitary waves in a chain with Lennard-Jones type nearest neighbor interaction are strongly localized and marginally stable in the high energy limit. In a damped and periodically driven chain we obtain numerically families of states whose behavior is similar to that of equally many oscillators. We observe a period doubling sequence in a one-solitary wave family and bifurcation to (quasi-) periodic motion in a family of two solitary waves. We conclude that the damped and driven chain admits asymptotically stable states living on a low-dimensional manifold in phase space. These results depend sensitively on the shape of the driving term.
Original languageEnglish
Pages (from-to)381-390
JournalPhysica D
Volume23
Issue number1-3
DOIs
Publication statusPublished - 1986

Fingerprint

Lennard-Jones
Solitary Waves
Solitons
Damped
solitary waves
Quasi-periodic Motion
Bifurcation (mathematics)
Period Doubling
period doubling
Asymptotically Stable
High Energy
Phase Space
Nearest Neighbor
Bifurcation
oscillators
Term
pulses
Interaction
Family
interactions

Cite this

Valkering, Theo P. ; van Opheusden, Joost H.J. / Interacting solitary waves in a damped driven Lennard-Jones chain. In: Physica D. 1986 ; Vol. 23, No. 1-3. pp. 381-390.
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Interacting solitary waves in a damped driven Lennard-Jones chain. / Valkering, Theo P.; van Opheusden, Joost H.J.

In: Physica D, Vol. 23, No. 1-3, 1986, p. 381-390.

Research output: Contribution to journalArticleAcademic

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T1 - Interacting solitary waves in a damped driven Lennard-Jones chain

AU - Valkering, Theo P.

AU - van Opheusden, Joost H.J.

PY - 1986

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N2 - It is shown analytically that pulse solitary waves in a chain with Lennard-Jones type nearest neighbor interaction are strongly localized and marginally stable in the high energy limit. In a damped and periodically driven chain we obtain numerically families of states whose behavior is similar to that of equally many oscillators. We observe a period doubling sequence in a one-solitary wave family and bifurcation to (quasi-) periodic motion in a family of two solitary waves. We conclude that the damped and driven chain admits asymptotically stable states living on a low-dimensional manifold in phase space. These results depend sensitively on the shape of the driving term.

AB - It is shown analytically that pulse solitary waves in a chain with Lennard-Jones type nearest neighbor interaction are strongly localized and marginally stable in the high energy limit. In a damped and periodically driven chain we obtain numerically families of states whose behavior is similar to that of equally many oscillators. We observe a period doubling sequence in a one-solitary wave family and bifurcation to (quasi-) periodic motion in a family of two solitary waves. We conclude that the damped and driven chain admits asymptotically stable states living on a low-dimensional manifold in phase space. These results depend sensitively on the shape of the driving term.

U2 - 10.1016/0167-2789(86)90144-2

DO - 10.1016/0167-2789(86)90144-2

M3 - Article

VL - 23

SP - 381

EP - 390

JO - Physica D

JF - Physica D

SN - 0167-2789

IS - 1-3

ER -