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  1. Zeitschrift für angewandte Mathematik und Physik
  2. Zeitschrift für angewandte Mathematik und Physik : Volume 57
  3. Zeitschrift für angewandte Mathematik und Physik : Volume 57, Issue 4, July 2006
  4. Instability of solitary waves on Euler’s elastica
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Zeitschrift für angewandte Mathematik und Physik : Volume 67
Zeitschrift für angewandte Mathematik und Physik : Volume 66
Zeitschrift für angewandte Mathematik und Physik : Volume 65
Zeitschrift für angewandte Mathematik und Physik : Volume 64
Zeitschrift für angewandte Mathematik und Physik : Volume 63
Zeitschrift für angewandte Mathematik und Physik : Volume 62
Zeitschrift für angewandte Mathematik und Physik : Volume 61
Zeitschrift für angewandte Mathematik und Physik : Volume 60
Zeitschrift für angewandte Mathematik und Physik : Volume 59
Zeitschrift für angewandte Mathematik und Physik : Volume 58
Zeitschrift für angewandte Mathematik und Physik : Volume 57
Zeitschrift für angewandte Mathematik und Physik : Volume 57, Issue 6, November 2006
Zeitschrift für angewandte Mathematik und Physik : Volume 57, Issue 5, September 2006
Zeitschrift für angewandte Mathematik und Physik : Volume 57, Issue 4, July 2006
Instability of solitary waves on Euler’s elastica
Mixtures of Euler’s fluids and second sound propagation in superfluid helium
Non-simultaneous quenching in a system of heat equations coupled at the boundary
On the spatial blow-up and decay for some nonlinear parabolic equations with nonlinear boundary conditions
Asymptotic profile of solutions to nonlinear dissipative evolution system with ellipticity
The small magnetic Prandtl number approximation suppresses magnetorotational instability
Transient film profile of thin liquid film flow on a stretching surface
Transient response of a semi-infinite piezoelectric layer with a surface permeable crack
Constitutive modeling of the mechanics associated with crystallizable shape memory polymers
A micromechanics-based Cosserat-type model for dense particulate solids
On nonlinear universal relations in nonlinear elasticity
Zeitschrift für angewandte Mathematik und Physik : Volume 57, Issue 3, May 2006
Zeitschrift für angewandte Mathematik und Physik : Volume 57, Issue 2, March 2006
Zeitschrift für angewandte Mathematik und Physik : Volume 57, Issue 1, November 2005
Zeitschrift für angewandte Mathematik und Physik : Volume 56
Zeitschrift für angewandte Mathematik und Physik : Volume 55
Zeitschrift für angewandte Mathematik und Physik : Volume 54
Zeitschrift für angewandte Mathematik und Physik : Volume 53
Zeitschrift für angewandte Mathematik und Physik : Volume 52
Zeitschrift für angewandte Mathematik und Physik : Volume 51
Zeitschrift für angewandte Mathematik und Physik : Volume 50
Zeitschrift für angewandte Mathematik und Physik : Volume 49
Zeitschrift für angewandte Mathematik und Physik : Volume 48

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Instability of solitary waves on Euler’s elastica

Content Provider SpringerLink
Author Il’ichev, Andrej T.
Copyright Year 2006
Abstract Stability of solitary waves in a thin inextensible and unshearable rod of infinite length is studied. Solitary-wave profile of the elastica of such a rod without torsion has the form of a planar loop and its speed depends on a tension in the rod. The linear instability of a solitary-wave profile subject to perturbations escaping from the plane of the loop is established for a certain range of solitary-wave speeds. It is done using the properties of the Evans function, an analytic function on the right complex half-plane, that has zeros if and only if there exist the unstable modes of the linearization around a solitary-wave solution. The result follows from comparison of the behaviour of the Evans function in some neighbourhood of the origin with its asymptotic at infinity. The explicit computation of the leading coefficient of the Taylor series of the Evans function near the origin is performed by means of the symbolic computer language.
Ending Page 566
Page Count 20
Starting Page 547
File Format PDF
ISSN 00442275
e-ISSN 14209039
Journal Zeitschrift für angewandte Mathematik und Physik
Issue Number 4
Volume Number 57
Language English
Publisher Birkhäuser-Verlag
Publisher Date 2006-02-23
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Euler’s elastica solitary wave Mathematical Methods in Physics Stability Evans function unstable eigenfunction orbital stability Rods (beams, columns, shafts, arches, rings, etc.) Theoretical and Applied Mechanics Solitary waves
Content Type Text
Resource Type Article
Subject Applied Mathematics Physics and Astronomy
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