Can 'soliton' attractors exist in realistic 3 +1-D conservative systems?

Chaos, Solitons and Fractals

Volumn 10, Issue 11, 1999, Pages 1917-1946

  Werbos, Paul J ^a  

^a NATIONAL SCIENCE FOUNDATION   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; ELEMENTARY PARTICLES; LAGRANGE MULTIPLIERS; NUCLEAR PHYSICS; QUANTUM THEORY;

FEYNMAN VERSION OF QUANTUM THEORY; STABLE ATTRACTORS;

SOLITONS;

EID: 0033229538     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(98)00162-3     Document Type: Article

References (44)

1. Makhankov, V. G., Rybakov, Yu. P. and Sanyuk, V. I., The Skyrme Model. Springer-Verlag, 1994.
2. Makhankov, V. G., Dynamics of classical solitons (in nonintegrable systems). Physics Reports, 1978, 35(1), 1-128.
3. Rajaraman, R., Some nonperturbative semiclassical methods in quantum field theory. Phys. Reports, 1975, 21(5), 227-317.
4. Cohen, T., Broniowski, W., The role of the delta isobar in chiral perturbation theory and hedgehog soliton models. Physics Letters, 1992, B292.
5. Chodos, A., Hadjimichael, E. and Tze, C., (eds.), Solitons in Nuclear and Elementary Particle Physics. World Scientific, 1984.
6. Mandl, F., Introduction to Quantum Field Theory. Wiley, 1959.
7. Zinn-Justin, J., Quantum Field Theory and Critical Phenomena, 3rd edn. Oxford University Press (Clarendon), Oxford, 1996.
8. Werbos, P., The Roots of Backpropagation: From Ordered Derivatives to Neural Networks and Political Forecasting. Wiley, 1994.
9. Grillakis, M., Shatah, J., Strauss, W., Stability theory of solitary waves in the presence of symmetry II. J. Functional Analysis, 1990, 94(2), 308-348, December.
10. Pego, R. L., Weinstein, M. I., Asymptotic stability of solitary waves. Communications in Math. Physics, 1994, 164, 305-349.
11. Eilenberger, G., Solitons. Springer-Verlag, 1983.
12. Whitham, G. B., Linear and Nonlinear Waves. Wiley, 1974.
13. Grebogi, C., Ott, E., Yorke, J., Chaos, strange attractors and fractal basin boundaries in nonlinear dynamics. Science, 1987, 238, 632-637, 30 October 1987.
14. Werbos, P., Chaotic solitons in conservative systems: can they exist? Chaos, Solitons and Fractals, 1993, 3(3), 321-326.
15. Penrose, R. and Rindler, W., Spinors and Space-Time. Cambridge University Press, Corrected Edition, 1987.
16. Werbos, P., New approaches to soliton quantization and stability for particle physics, xxx.lanl.gov/form. Paper number patt-sol 9804003, which requires "Other Groups" set to nlin-sys.
17. Narendra, K. and Annaswamy, A., Stable Adaptive Systems. Prentice-Hall, Englewood NJ, 1989.
18. Goldhaber, A. S., Connection of spin and statistics for charge-monopole composites. Physical Review Letters, 1976, 36(19), 1122-1125, May 10.
19. Wilczek, F. Phys Rev Lett., 1982, 48, 1146.
20. Lovelock, D. and Rund, H., Tensors, Differential Forms and Variational Principles. Wiley, 1975.
21. Gelfand, I. M. and Fomin, S. V., Calculus of Variations, Revised English Edition. Prentice-Hall, NJ, 1963.
22. Werbos, P., Self-organization: Re-examining the basics and an alternative to the Big Bang. In Origins: Brain and Self-Organization, ed. K. Pribram. Erlbaum, 1994.
23. Zastavenko, L. G., Particle-like solutions for a nonlinear wave equation, Prikladnaya Matematika i Mechanika, 29, 430-439 (in Russian, see JETP translations).
24. Bogolubsky, I. L., On spinor soliton stability. Physics Letters, 1979, 73A(2) (September 1979).
25. Bryson, A. and Ho, Y. C., Applied Optimal Control. Ginn, 1969.
26. Saxon, D. S., Elementary Quantum Mechanics. Holden-Day, 1968.
27. Titchmarsh, E. C., Eigenfunctional Expansions Associated with Second-Order Differential Equations. Oxford Clarendon Press, 1962. (See Books on Demand, Ann Arbor, MI.).
28. Weinberg, S., Gravitation and Cosmology. Wiley, 1972.
29. Costa de Beauregard, O., Relativity and probability, classical and quantal. In Probability in the Sciences, ed. E. Agazzi. Kluwer, 1988, pp. 183-202. (See also many more detailed later papers by the same author).
30. Werbos, P., Bell's theorem: the forgotten loophole and how to exploit it. In Bell's Theorem, Quantum Theory and Conceptions of the Universe, ed. M. Kafatos. Kluwer, 1989.
31. Werbos, P., An approach to the realistic explanation of quantum mechanics. Nuovo Cimento Letters, 1973, 29B, 105-109, (September 8, 1973).
32. Segre, E., Nuclei and Particles. W. A. Benjamin, New York, 1965, (Section 6.6).
33. Adler, R., Bazin, M. and Schiffer, M., Introduction to General Relativity. McGraw-Hill, 1965.
34. Press, W., Flannery, B., Teukolsky, S. and Vetterling, W., Numerical Recipes in C. Cambridge University Press, 1988.
35. Sterman, G., An Introduction to Quantum Field Theory. Cambridge University Press, 1993, (Equation 3.39).
36. Schwinger, J., Particles, Sources and Fields. Addison-Wesley, 1970.
37. Schwinger, J., Sources and magnetic charge. Physical Review, 1968, 173(5), 1536-1544, (September 25, 1968).
38. Werbos, P., Chaotic solitons and the foundations of physics: a potential revolution. Applied Mathematics and Computation, 1993, 56, 289-340, July 1993.
39. Jezabek, M., Kuhn, J. H., Peter, M., Sumino, Y. and Teubner, T. The perturbative QCD potential and the ttbar threshold, hep-ph/9802373. xxx.lanl.gov, 1998.
40. Itzykson, C. and Drouffe, J., Statistical Field Theory, paperback edition. Cambridge University Press, 1991.
41. White, D. and Sofge, D., (eds.), Handbook of Intelligent Control. Van Nostrand, 1992, (Section 13.6).
42. Karny, M., Warwick, K. and Kurkova, V., (eds.), Dealing with Complexity. Springer, 1997, (Chapter 18, Section 4.3).
43. Kogut, J. et al., R7 and R21. In Lattice Gauge Theories and Monte Carlo Simulations, ed. C. Rebbi. World Scientific, 1983.
44. Taylor, J., The renormalization constants in perturbation theory. Nuovo Cimenta, 1960,17(5), 695-702, (September 1960).