### 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 language | English |
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Pages (from-to) | 2099-2116 |

Number of pages | 18 |

Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 355 |

Issue number | 1732 |

Publication status | Published - Nov 15 1997 |

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### ASJC Scopus subject areas

- General

### Cite this

**Static solitary waves as limits of discretization : A plausible argument.** / Domokos, G.

Research output: Contribution to journal › Article

*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 355, no. 1732, pp. 2099-2116.

}

TY - JOUR

T1 - Static solitary waves as limits of discretization

T2 - A plausible argument

AU - Domokos, G.

PY - 1997/11/15

Y1 - 1997/11/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=3142560036&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3142560036&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:3142560036

VL - 355

SP - 2099

EP - 2116

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0962-8428

IS - 1732

ER -