Static solitary waves as limits of discretization: A plausible argument

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Abstract

We investigate special limits of the classical Euler buckling problem, arguing that the solution-family 'imitating' (without mass forces) the propagation of a dynamic solitary wave cannot be obtained as a limit from Euler's problem, only from its discretized version. Although we can not prove this claim rigorously, we prove other related statements that make the conjecture strongly plausible. Our results yield access to some open questions related to the discretized problem; also they show some new aspects of spatially chaotic behaviour.

Original languageEnglish
Pages (from-to)2099-2116
Number of pages18
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume355
Issue number1732
Publication statusPublished - Nov 15 1997

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Solitary Waves
Solitons
Buckling
Euler buckling
solitary waves
Discretization
Euler
Chaotic Behavior
propagation
Propagation

ASJC Scopus subject areas

  • General

Cite this

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title = "Static solitary waves as limits of discretization: A plausible argument",
abstract = "We investigate special limits of the classical Euler buckling problem, arguing that the solution-family 'imitating' (without mass forces) the propagation of a dynamic solitary wave cannot be obtained as a limit from Euler's problem, only from its discretized version. Although we can not prove this claim rigorously, we prove other related statements that make the conjecture strongly plausible. Our results yield access to some open questions related to the discretized problem; also they show some new aspects of spatially chaotic behaviour.",
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