Dispersive Behaviours in Complex Structures

Butuc, Irina; Ghizdovăţ, Vlad

doi:10.2478/bipmf-2021-0015

Abstract

In the framework of the Scale Relativity Theory, a fractal Korteweg-de Vries-type equation for describing dispersive behaviours of any complex structure is obtained. In the one-dimensional case, the general solution of this equation show that the dispersive behaviours of any complex structure are given by means of cnoidal oscillation modes. Through these modes degeneration, dispersive behaviours of soliton, soliton-package, harmonic etc. result.

References

Armitage J.V., Elliptic Functions, Cambridge, Cambridge University Press (2006).
Search in Google Scholar Back to article
Aronstein D.L., Stroud C.R., Fractional Wave-Function Revivals in the Infinite Square Well, Physical Review A 55, 6, 4526-4537 (1997).10.1103/PhysRevA.55.4526
Search in Google Scholar Back to article
Ball P., The Self-Made Tapestry: Pattern Formation in Nature, Oxford, Oxford University Press (1999).
Search in Google Scholar Back to article
Ball P., Critical Mass: How One Thing Leads to Another, London, Macmillan (2004).
Search in Google Scholar Back to article
Bar-Yam Y., Dynamics of Complex Systems, Boston, Addison-Wesley (1997).
Search in Google Scholar Back to article
Butuc I., Gavriluț A., Gavriluț G., Duceac L.D., Differentiable and Non-Differentiable Cellular Neural Networks with Implication in the Bacterial Growth Process. Properties (II), Buletinul Institutului Politehnic Iași, Secția Matematică. Mecanică Teoretică. Fizică, 62(66), 1, 77-84 (2016).
Search in Google Scholar Back to article
Cristescu C.P., Dinamici Neliniare și Haos, Fundamente Teoretice și Aplicații, Bucharest, Romanian Academy Publishing House (2008).
Search in Google Scholar Back to article
Gleick J., Chaos: Making a New Science, New York, Open Road Media (2011).
Search in Google Scholar Back to article
Holland J.H., Adaptation in Natural and Artificial Systems, MIT Press, Cambridge, 1992.10.7551/mitpress/1090.001.0001
Search in Google Scholar Back to article
Jackson A.A., Perspectives of Nonlinear Dynamics, vol. 1 & 2, New York, Cambridge University Press (1993).
Search in Google Scholar Back to article
Mercheș I., Agop M., Differentiability and Fractality in Dynamics of Physical Systems, Singapore, World Scientific (2015).10.1142/9606
Search in Google Scholar Back to article
Mitchell M., Complexity: A Guided Tour, Oxford, Oxford University Press (2009).
Search in Google Scholar Back to article
Nica P., Agop M., Gurlui S., Bejinariu C., Focşa C., Characterization of Aluminum Laser Produced Plasma by Target Current Measurements, Japanese Journal of Applied Physics 51, 106102 (2012).10.1143/JJAP.51.106102
Search in Google Scholar Back to article
Pompilian O.G., Gurlui S., Nemec P., Nazabal V., Ziskind M. et al., Plasma Diagnostics in Pulsed Laser Deposition of GaLaS Chalcogenides, Applied Surface Science 278, 352-356 (2013).10.1016/j.apsusc.2012.11.069
Search in Google Scholar Back to article
Thurner S., Hanel R., Klimek P., Introduction to the Theory of Complex Systems, Oxford, Oxford University Press (2018).10.1093/oso/9780198821939.001.0001
Search in Google Scholar Back to article
Toda M., Theory of Nonlinear Lattices, New York, Springer-Verlag (1981).10.1007/978-3-642-96585-2
Search in Google Scholar Back to article
Whitham G.B., Linear and Nonlinear Waves, New York, John Wiley and Sons (1974).
Search in Google Scholar Back to article

Dispersive Behaviours in Complex Structures

Abstract

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