Renormalization-group method for reduction of evolution equations; invariant manifolds and envelopes

Annals of Physics

Volumn 280, Issue 2, 2000, Pages 236-298

  Ei, Shin Ichiro ^a   Fujii, Kazuyuki ^a   Kunihiro, Teiji ^b  

^a YOKOHAMA CITY UNIVERSITY   (Japan)

^b RYUKOKU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0345856722     PISSN: 00034916     EISSN: None     Source Type: Journal    
DOI: 10.1006/aphy.1999.5989     Document Type: Article

References (67)

1. Stueckelberg E. C. G., Petermann A. Helv. Phys. Acta. 26:1953;499.
2. Ma S. K. Modern Theory of Critical Phenomena. 1976;Benjamin, New York.
3. D. V. Shirkov, hep-th/9602024; hep-th/9903073.
4. Wilson K. G., Fisher M. E. Phys. Rev. Lett. 28:1972;240.
5. Wegner F., Houghton A. Phys. Rev. A. 8:1973;401.
6. Polchinski J. Nucl. Phys. B. 231:1984;269.
7. Nambu Y., Jona-Lasinio G. Phys. Rev. 122:1961;345.
8. Klevanski S. Rev. Mod. Phys. 64:1992;649.
9. Weinberg S. The Quantum Theory of Fields, II. 1996;Cambridge Univ. Press, Cambridge.
10. Wetterich C. Phys. Lett. B. 301:1993;90.
11. Morris T. R. Int. J. Mod. Phys. A. 9:1994;2411.
12. Aoki K.-I. Prog. Theor. Phys. Suppl. 131:1998;129.
13. Prog. Theor. Phys. Suppl. 131:1998.
14. Boltzmann L. Lectures on GAs Theory. 1964;Univ. of Calfornia Press, Berkeley.
15. N. N. Bogoliubov, in, Studies in Statistical Mechanics, (, J. de Boer and G. E. Uhlenbeck, Eds.), Vol, 1, North-Holland, Amsterdam.
16. Kuramoto Y. Prog. Theor. Phys. Suppl. 99:1989;244.
17. Chapman S., Cowling T. G. The Mathematical Theory of Non-Uniform Gases. 1970;Cambrdige Univ. Press, Cambridge.
18. Glansdorff P., Prigogine I. Thermodynamic Theory of Structure, Stability, and Fluctuations. 1971;Wiley, London.
19. Kuramoto Y. Chemical Oscillations, Waves, and Turbulence. 1984;Springer-Verlag, New York/Berlin.
20. Guckenheimer J., Holmes P. Nonlinear Oscillators, Dynamical Systems, and Bifurcations of Vector Fields. 1983;Springer-Verlag, New York/Berlin.
21. Goldenfeld N., Martin O., Oono Y. J. Sci. Comp. 4:1989;4.
22. Chen L. Y., Goldenfeld N., Oono Y., Paquette G. Physica A. 204:1994;111.
23. Paquette G., Chen L. Y., Goldenfeld N., Oono Y. Phys. Rev. Lett. 72:1994;76.
24. Bricmont J., Kupiainen A. Comm. Math. Phys. 150:1992;193.
25. Kunihiro T. Prog. Theor. Phys. 94:1995;503.
26. Kunihiro T. Prog. Theor. Phys. 97:1997;179.
27. Kunihiro T. Phys. Rev. D. 57:1998;R2035.
28. Graham R. Phys. Rev. Lett. 76:1996;2185.
29. Oono Y. Structural stability of spinodal decomposition. 1996.
30. Sasa S. Physica D. 108:1997;45.
31. Maruo T., Nozaki K., Yoshimori A. Prog. Theor. Phys. 101:1999;243.
32. Kuramoto Y. Prog. Theor. Phys. 55:1976;356.
33. de Vega H. J., Salgado J. F. J. Phys. Rev. D. 56:1997;6524.
34. Taruya A., Nambu Y. Phys. Lett. B. 428:1998;37.
35. D. Boyanovsky, H. J. de Vega, R. Holman, and, M. Simionato, hep-ph/9809346; D. Boyanovsky and H. J. de Vega, Phys. Rev. D, 59, (1999), 105, 019.
36. D. Boyanovsky, H. J. de Vega, R. Holman, and, M. Simionato, hep-ph/9809346; D. Boyanovsky and H. J. de Vega, Phys. Rev. D, 59, (1999), 105, 019.
37. O. Pashko, and, Y. Oono, The Boltzmann equation is a renormalization group equation, preprint, 1996.
38. Frasca M. Phys. Rev. A. 56:1997;1549.
39. S. I. Tzenov, and, P. L. Colestock, preprint, FERMILAB-PUB-98-258; S. I. Tzenov, preprint, FERMILAB-PUB-98-275.
40. S. I. Tzenov, and, P. L. Colestock, preprint, FERMILAB-PUB-98-258; S. I. Tzenov, preprint, FERMILAB-PUB-98-275.
41. Yamaguchi Y. Y., Nambu Y. Prog. Theor. Phys. 100:1998;199.
42. Kunihiro T., Matsukidaira J. Phys. Rev. E. 57:1998;4817.
43. Bogoliubov N. N., Mitropolski Y. A. Asymptotic Methods in the Theory of Nonlinear Oscillations. 1961;Gordon & Breach, New York.
44. Kovalev V. F., Pustovalov V. V., Shirkov D. V. J. Math. Phys. 39:1998;1170.
45. Kawasaki K., Ohta T. Physica A. 116:1982;573.
46. Carr J., Pego R. L. Comm. Pure Appl. Math. 42:1989;523.
47. Ei S.-I., Ohta T. Phys. Rev. E. 50:1994;4672.
48. Fusco G., Hale J. J. Dynam. Diff. Eq. 1:1989;75.
49. Landau L. D., Lifshitz E. M. Quantum Mechanics. 1977;Pergamon, Oxford.
50. Pego R. L., Weinstein M. I. Comm. Math. Phys. 164:1994;305.
51. Takens F. Inst. Hautes Études Sci. Publ. Math. 43:1974;47.
52. Wiggins S. Introduction to Applied Nonlinear Dynamical Systems and Chaos. 1990;Springer-Verlag, New York.
53. Bogdanov R. I. Funct. Anal. Appl. 9:1975;144.
54. Glansdorff P., Prigogine I. Thermodynamic Theoryof Structure, Stability, and Fluctuations. 1971;Wiley, London.
55. Lotka A. J. J. Am. Chem. Soc. 42:1920;1595.
56. T. Kunihiro, unpublished, 1996.
57. Frame J. S. J. Theor. Biol. 43:1974;73.
58. Haken H. Advanced Synergitics. 1983;Springer-Verlag, New York/Berlin.
59. Nishiura Y. Nonlinear Problems. I. Mathematics of Pattern Formation. 1998;Iwanami Shoten, Tokyo.
60. Lorenz E. N. J. Atmos. Sci. 20:1963;130.
61. Mori H. Prog. Theor. Phys. 33:1965;423.
62. J. Meyer, G. Papp, H.-J. Pirner, and, T. Kunihiro, nucl-th/9908019, to be published in, Phys. Rev. C, (2000).
63. J. O. Andersen, and, M. Strickland, cond-mat/9811096.
64. Garcia S., Guralnik G. S., Lawson J. W. Phys. Lett. B. 333:1994;119.
65. Chen L.-Y., Goldenfeld N. Phys. Rev. 51:1995;5577.
66. Whitham G. B. Linear and Non-linear Waves. 1977;Wiley, New York.
67. K. Takasaki, Seminar, RIMS of Kyoto University, Applications of RG Methods in Mathematical Sciences, July 21-23, 1999.