Resonant triad interactions in symmetric systems

John Guckenheimer; Alex Mahalov

doi:10.1016/0167-2789(92)90040-T

Resonant triad interactions in symmetric systems

John Guckenheimer
, Alex Mahalov

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We analyse resonant triad interactions in symmetric systems. The case of coupling at quadratic order in amplitudes and the case of coupling at cubic order are considered. We study modulated travelling waves and heteroclinic cycles in amplitude equations and we discuss their stability types. We describe possible dynamical regimes and spatial patterns arising from triad interactions of long waves in rapidly rotating Hagen-Poiseuille flow.

Original language	English (US)
Pages (from-to)	267-310
Number of pages	44
Journal	Physica D: Nonlinear Phenomena
Volume	54
Issue number	4
DOIs	https://doi.org/10.1016/0167-2789(92)90040-T
State	Published - Jan 2 1992
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/0167-2789(92)90040-T

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title = "Resonant triad interactions in symmetric systems",

abstract = "We analyse resonant triad interactions in symmetric systems. The case of coupling at quadratic order in amplitudes and the case of coupling at cubic order are considered. We study modulated travelling waves and heteroclinic cycles in amplitude equations and we discuss their stability types. We describe possible dynamical regimes and spatial patterns arising from triad interactions of long waves in rapidly rotating Hagen-Poiseuille flow.",

author = "John Guckenheimer and Alex Mahalov",

note = "Funding Information: This work was supported by the Air Force Office of Scientific Research under contracts AFOSR-89-0346 and AFOSR-89-0226. J. Guckenheimer was supported by NSF, AFOSR and the Army Research Office through the Mathematical Sciences Institute at Cornell University. A Mahalov is supported by an IBM Watson Fellowship. We would like to thank Sidney Leibovich for very helpful discussions.",

year = "1992",

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doi = "10.1016/0167-2789(92)90040-T",

language = "English (US)",

volume = "54",

pages = "267--310",

journal = "Physica D: Nonlinear Phenomena",

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TY - JOUR

T1 - Resonant triad interactions in symmetric systems

AU - Guckenheimer, John

AU - Mahalov, Alex

N1 - Funding Information: This work was supported by the Air Force Office of Scientific Research under contracts AFOSR-89-0346 and AFOSR-89-0226. J. Guckenheimer was supported by NSF, AFOSR and the Army Research Office through the Mathematical Sciences Institute at Cornell University. A Mahalov is supported by an IBM Watson Fellowship. We would like to thank Sidney Leibovich for very helpful discussions.

PY - 1992/1/2

Y1 - 1992/1/2

N2 - We analyse resonant triad interactions in symmetric systems. The case of coupling at quadratic order in amplitudes and the case of coupling at cubic order are considered. We study modulated travelling waves and heteroclinic cycles in amplitude equations and we discuss their stability types. We describe possible dynamical regimes and spatial patterns arising from triad interactions of long waves in rapidly rotating Hagen-Poiseuille flow.

AB - We analyse resonant triad interactions in symmetric systems. The case of coupling at quadratic order in amplitudes and the case of coupling at cubic order are considered. We study modulated travelling waves and heteroclinic cycles in amplitude equations and we discuss their stability types. We describe possible dynamical regimes and spatial patterns arising from triad interactions of long waves in rapidly rotating Hagen-Poiseuille flow.

UR - https://www.scopus.com/pages/publications/0038868531

UR - https://www.scopus.com/pages/publications/0038868531#tab=citedBy

U2 - 10.1016/0167-2789(92)90040-T

DO - 10.1016/0167-2789(92)90040-T

M3 - Article

SN - 0167-2789

VL - 54

SP - 267

EP - 310

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 4

ER -

Resonant triad interactions in symmetric systems

Abstract

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