Reduction and reconstruction for self-similar dynamical systems

Nonlinearity

Volumn 16, Issue 4, 2003, Pages 1257-1275

  Rowley, Clarence W ^a   Kevrekidis, Ioannis G ^b   Marsden, Jerrold E ^c   Lust, Kurt ^d  

^a Princeton University   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^d UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242308944     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/4/304     Document Type: Article

References (23)

1. Aronson D G, Betelu S I and Kevrekidis I G 2001 Going with the flow: a Lagrangian approach to self-similar dynamics and its consequences PNAS submitted (Preprint nlin.A0/0111055)
2. Barenblatt G I 1996 Scaling, Self-Similarity, and Intermediate Asymptotics (Cambridge: Cambridge University Press)
3. Budd C J and Piggott M D 2001 The geometric integration of scale-invariant ordinary and partial differential equations J. Comp. Appl. Math. 128 399-422
4. Doedel E, Keller H B and Kernevez J P 1991 Numerical analysis and control of bifurcation problems (II) Bifurcation in infinite dimensions Int. J. Bifurcation Chaos 1 745-72
5. Duistermaat J J and Kolk J A C 1999 Lie Groups (Berlin: Springer)
6. Gear C W, Kevrekidis I G and Theodoropoulos C 2002 Coarse integration/bifurcation analysis via microscopic simulators: micro-Galerkin methods Comp. Chem. Engng 26 941-63
7. Goldenfeld N 1992 Lectures on Phase Transitions and the Renormalization Group (Reading, MA: Addison-Wesley)
8. Kirby M and Armbruster D 1992 Reconstructing phase space from PDE simulations Z. Angew. Math. Phys. 43 999-1022
9. Lust K, Roose D, Spence A and Champneys A R 1998 An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions SIAM J. Sci. Comput. 19 1188-209
10. Lust K and Rowley C W and Kevrekidis I G On the computation and stability analysis of self-similar solutions in preparation
11. Marsden J E 1990 Lectures on Mechanics vol 174 (London Mathematical Society Lecture Note Series) (Cambridge: Cambridge University Press)
12. Marsden J E, Montgomery R and Ratiu T S 1990 Reduction, symmetry, and phases in mechanics Mem. Amer. Math. Soc. 88
13. Marsden J E and Ratiu T S 1994 Introduction to mechanics and symmetry Texts in Applied Mathematics 2nd edn, vol 17 (Berlin: Springer)
14. McLaughlin D W, Papanicolaou G C, Sulem C and Sulem P L 1986 Focusing singularity of the cubic Schrödinger equation Phys. Rev. A 34 1200-10
15. Olver P J 1986 Applications of lie groups to differential equations Graduate Texts in Mathematics vol 107 (Berlin: Springer)
16. Othmer H G and Stevens A 1997 Aggregation, blowup, and collapse: the ABC's of taxis in reinforced random walks SIAM J. Appl. Math. 57 1044-81
17. Ovsiannikov L V 1982 Group Analysis of Differential Equations (New York: Academic)
18. Rowley C W and Marsden J E 2000 Reconstruction equations and the Karhunen-Loève expansion for systems with symmetry Phys. D 42 1-19
19. Runborg O, Theodoropoulos C and Kevrekidis I G 2002 Effective bifurcation analysis: a time-stepper-based approach Nonlinearity 15 491-511
20. Shroff G and Keller H B 1993 Stabilization of unstable procedures: the recursive projection method SIAM J. Numer. Anal. 30 1099-120
21. Siettos C, Kevrekidis I G and Kevrekidis P G 2003 Focusing revisited: a renormalization/bifurcation approach Nonlinearity 16 497-506
22. Whitham G B 1974 Linear and Nonlinear Waves (New York: Wiley)
23. Zakharov V E and Shvets V F 1988 Nature of wave collapse in the critical case JETP Lett. 47 275-8