Spectral stability of local deformations of an elastic rod: Hamiltonian formalism

SIAM Journal on Mathematical Analysis

Volumn 36, Issue 6, 2005, Pages 1726-1741

  Lafortune, S ^a   Lega, J ^b  

^a School of Business   (United States)

^b University of Arizona   (United States)

Author keywords

Elastic filament; Hamiltonian methods; Spectral stability

Indexed keywords

ELASTIC FILAMENTS; HAMILTONIAN METHODS; SPECTRAL STABILITY;

FUNCTIONS; NONLINEAR EQUATIONS;

HAMILTONIANS;

EID: 27844536860     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141004439350     Document Type: Article

References (23)

1. E. KUZNETSOV, C. D. LEVERMORE, AND N. ERCOLANI, EDS., Advances in Nonlinear Mathematics and Science: A Special Issue to Honor Vladimir Zakharov, Phys. D, 152-153 (2001).
2. J. W. EVANS, Nerve axon equations. IV. The stable and unstable impulse, Indiana Univ. Math. J., 24 (1975), pp. 1169-1190.
3. C. K. R. T. JONES, Stability of the travelling wave solution to the FitzHugh-Hagumo equation, Trans. Amer. Math. Soc., 286 (1984), pp. 431-469.
4. E. YANAGIDA, Stability of fast traveling pulse solutions of the FitzHugh-Nagumo equations, J. Math. Biol., 22 (1985), pp. 81-104.
5. J. ALEXANDER, R. GARDNER AND C. JONES, A topological invariant arising in the stability analysis of travelling waves, J. Reine Angew. Math., 410 (1990), pp. 167-212.
6. R. PEGO AND M. WEINSTEIN, Eigenvalues, and instabilities of solitary waves, Phil. Trans. R. Soc. London Ser. A, 340 (1992), pp. 47-94.
7. R. A. GARDNER AND K. ZUMBRUN, The gap lemma and geometric criteria for instability of viscous shock profiles, Comm. Pure Appl. Math., 51 (1998), pp. 797-855.
8. T. KAPITULA AND B. SANDSTEDE, Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations, Phys. D, 124 (1998), pp. 58-103.
9. B. SANDSTEDE, Stability of travelling waves, in Handbook of Dynamical Systems II: Towards Applications, B. Fiedler, ed., North-Holland, Amsterdam, 2002, pp. 983-1055.
10. T. J. BRIDGES, G. DERKS, AND G. GOTTWALD, Stability and instability of solitary waves of the fifth-order KdV equation: A numerical framework, Phys. D, 172 (2002), pp. 190-216.
11. M. GRILLAKIS, J. SHATAH, AND W. STRAUSS, Stability theory of solitary waves in the presence of symmetry, I, J. Funct. Anal., 74 (1987), pp. 160-197.
12. M. GRILLAKIS, J. SHATAH, AND W. STRAUSS, Stability theory of solitary waves in the presence of symmetry, II, J. Funct. Anal., 94 (1990), pp. 308-348.
13. A. GORIELY AND M. TABOR, Nonlinear dynamics of filaments II: Nonlinear analysis, Phys. D, 105 (1997), pp. 45-61.
14. S. LAFORTUNE AND J. LEGA, Instability of local deformations of an elastic rod, Phys. D, 182 (2003), pp. 103-124.
15. J. LEGA AND A. GORIELY, Pulses, fronts, and oscillations of an elastic rod, Phys. D, 132 (1999), pp. 373-391.
16. P. OLVER, Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, 1993.
17. G. DANGELMAYR AND E. KNOBLOCH, The Takens-Bogdanov bifurcation with O(2)-symmetry, Phil. Trans. Roy. Soc. London Ser. A, 322 (1987), pp. 243-279.
18. J. CARMINATI AND K. Vu, Symbolic computation and differential equations: Lie symmetries, J. Symbolic Comput., 29 (2000), pp. 95-116.
19. E. CODDINGTON AND N. LEVINSON, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.
20. M. REED AND B. SIMON, Methods of Modern Mathematical Physics. IV. Analysis of Operators, Academic Press, New York, 1978.
21. P. LAX, Linear Algebra, John Wiley & Sons, New York, 1996.
22. D. HENRY, Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag, New York, 1981.
23. A. GORIELY, M. NIZETTE, AND M. TABOR, On the dynamics of elastic strips, J. Nonlinear Sci., 11 (2001), pp. 3-45.