Stability Theory of Solitary Loops Propagating Along Euler’s Elastica

DOI10.1007/978-3-030-11665-1_15zbMath1429.74064OpenAlexW2921050822MaRDI QIDQ5214643

Andrej Il'ichev

Publication date: 7 February 2020

Published in: Dynamical Processes in Generalized Continua and Structures (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-11665-1_15

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Dynamical systems in solid mechanics (37N15)

Cites Work

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• Instability of solitons under flexure and twist of an elastic rod
• Stability theory of solitary waves in the presence of symmetry. I
• Kirchhoff's theory of rods
• On the dynamics of rods in the theory of Kirchhoff and Clebsch
• Instability of local deformations of an elastic rod
• On the dynamics of flexure and stretch in the theory of elastic rods
• Conditional stability of solitary waves propagating in elastic rods
• On the interaction of solitary waves of flexure in elastic rods
• Hamiltonian dynamics of an elastica and the stability of solitary waves
• Instability of solitary waves on Euler's elastica
• Stability of the Travelling Wave Solution of the Fitzhugh-Nagumo System
• Travelling waves in hyperelastic rods
• The Evans Function and Generalized Melnikov Integrals
• Eigenvalues, and instabilities of solitary waves
• Stability of solitary waves in nonlinear composite media

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