Geometry and transport in a model of two coupled quadratic nonlinear waveguides

Chaos

Volumn 18, Issue 1, 2008, Pages

  Stirling, James R ^a   Bang, Ole ^b   Christiansen, Peter L ^b   Zakynthinaki, Maria S ^a,c   Johansen, Steffen Kjær ^d  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^c UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^d Woven Reality ApS   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 41549135580     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2840461     Document Type: Article

References (26)

1. V. M. Agranovich and J. B. Page, " Fermi resonance interface modes and bistable energy transmission through the interface.," Phys. Lett. A 183, 395 (1993).
2. S. A. Dubovskii and A. V. Orlov, " New type of nonlinear interface waves under the conditions of Fermi resonance of the vibrations of adjoining crystals.," Fiz. Tverd. Tela (Leningrad) 0367-3294 38, 1221 (1996) S. A. Dubrovskii and A. V. Orlov, [Phys. Solid State 38, 675 (1996)].
3. T. Peschel, U. Peschel, and F. Lederer, " Solitary waves in Bragg gratings with a quadratic nonlinearity.," Phys. Rev. E 55, 4730 (1997).
4. P. D. Miller and O. Bang, " Macroscopic dynamics in quadratic nonlinear lattices.," Phys. Rev. E 57, 6038 (1998).
5. O. Bang, P. L. Christiansen, and C. B. Clausen, " Stationary solutions and self trapping in discrete quadratic nonlinear systems.," Phys. Rev. E 56, 7257 (1997).
6. V. I. Arnold, Mathematical Methods of Classical Mechanics, in Graduate Texts in Mathematics (Springer-Verlag, Berlin, 1989).
7. G. Haller and S. Wiggins, " Geometry and chaos near resonant equilibria of 3-DOF Hamiltonian systems.," Physica D 90, 319 (1996).
8. G. Haller, Chaos Near Resonance, Applied Mathematical Sciences (Springer, New York, 1999), Vol. 138.
9. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, Applied Mathematical Sciences (Springer, Berlin, 1992), Vol. 138.
10. A. Litvak-Hinenzon and V. Rom-Kedar, " Resonant tori and instabilities in Hamiltonian systems.," Nonlinearity 15, 1149 (2002).
11. A. Litvak-Hinenzon and V. Rom-Kedar, " On energy surfaces and the resonance web.," SIAM J. Appl. Dyn. Syst. 3, 525 (2004).
12. A. Litvak-Hinenzon and V. Rom-Kedar, " Parabolic resonances in 3 d.o.f. near integrable Hamiltonian systems.," Physica D 164, 213 (2004).
13. J. D. Meiss, " Symplectic maps, variational principles, and transport.," Rev. Mod. Phys. 64, 795 (1992).
14. V. Rom-Kedar and S. Wiggins, " Transport in two-dimensional maps.," Arch. Ration. Mech. Anal. 109, 239 (1990).
15. V. Rom-Kedar, " Transport in a class of n-d.o.f. systems.," in Hamiltonian Systems with Three or More Degrees of Freedom (S'Agar'o, 1995) (Kluwer Academic, Dordrecht, 1999), pp. 538-543.
16. S. Wiggins, " On the geometry of transport in phase space 1. Transport in a k-degree-of-freedom Hamiltonian system, 2k∞," Physica D 44, 471 (1990).
17. S. Wiggins, Chaotic Transport in Dynamical Systems, Interdisciplinary Applied Mathematics (Springer-Verlag, Berlin, 1992).
18. G. M. Zaslavsky, R. Z. Sagdeev, D. A. Usikov, and A. A. Chernkow, Weak Chaos and Quasi-Regular Patterns, Cambridge Nonlinear Science (Cambridge University Press, Cambridge, 1991), Vol. 1.
19. A. Delshams, R. de la Llave, and T. M. Seara, " Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows.," Adv. Math. 202, 64 (2006).
20. A. Delshams, R. de la Llave, and T. M. Seara, " Geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Heuristics and rigorous verification on a model.," Mem. Am. Math. Soc. 179, 1 (2006).
21. A. Delshams, R. de la Llave, and T. M. Seara, " A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of the torus.," Commun. Math. Phys. 209, 353 (2000).
22. J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport, Cambridge Texts in Applied Mathematics (Cambridge University Press, Cambridge, 1989).
23. J. R. Stirling, " Dynamical systems models of patchiness in estuaries.," Ph.D. thesis, Department of Mathematical Sciences, Loughborough University, UK, 1999.
24. J. R. Stirling, " Transport and bifurcation in a non area preserving 2 dimensional map with applications to the discharge of pollution in an estuarine flow.," Physica D 144, 169 (2000).
25. J. R. Stirling, " Nonlinear dynamics, transport and the patchiness of clouds of pollution in an estuarine fluid flow.," Discrete Contin. Dyn. Syst., Ser. B 3, 263 (2003).
26. A. Back, J. Guckenheimer, M. R. Myers, F. J. Wicklin, and P. A. Worfolk, " DsTool: Computer assisted exploration of dynamical systems.," Not. Am. Math. Soc. 39, 303 (1992).