A special class of DRIP media with hysteresis
Keywords:
hysteresis operator, DRIP media, interacting waves, Preisach model, soliton theoryAbstract
Since the interaction phenomenon for waves of arbitrary shape and amplitude is a property of the transmitting medium rather than of the particular wave profiles, Seymour and Varley named as DRIP the media that do not remember the interaction process. In such media the profile of the interacting waves is affected by the interactions with hysteresis. The waves exhibit the solitonic features, but in contrast to solitons, the waves distort as they propagate by an amount that is altered by the interaction. The hysteretic effect is to alter the arrival time of their fronts at any point.
References
MUNTEANU, L., DONESCU, St., Introduction to Soliton Theory: Applications to Mechanics, Book Series Fundamental Theories of Physics, Vol. 143, Kluwer Academic Publishers, 2004.
FERMI, E., PASTA, J.R., ULAM, S.M., Studies of nonlinear problems, Technical Report LA1940, Los Alamos Sci. Lab., 1955.
FERMI, E., PASTA, J. R., ULAM, S.M., in: Collected Papers of Enrico Fermi, Vol. 2, E. Fermi, The Univ. of Chicago Press, Chicago, 1965.
SEYMOUR, B.R., VARLEY, E., Exact solutions describing soliton-like interactions in a nondispersive medium, SIAM J. Appl. Math., 42, 4, pp. 804–821, 1982
KAPLAN, A.E., Hysteresis reflection and refraction at the nonlinear interface- a new class of nonlinear optics, JETP Lett., 24, pp. 114–117, 1976.
YE, F., KARTASHOV, Y.V., TORNER, L., Vector soliton fission by reflection at nonlinear interfaces, Optics Letters, 32, 4, pp. 394–395, 2007.
KRANOSELSKII, M.A., POKROVSKII, A.V., Systems with Hysteresis, Springer, Berlin, 1989 (in Russian, ed. Nauka, Moscow 1983).
K?MURA, Y., Nonlinear semi-groups in Hilbert space, Journal of the Mathematical Society of Japan, 19, 4, pp. 493–507, 1967.
CRANDALL, M.C., LIGGETT, T.M., Generation of semigroups of nonlinear transformations on general Banach spaces, Amer. J. Math., 93, pp. 265–298, 1971.
BARBU, V., Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, Leyden, 1976.
IONESCU, M.F., MUNTEANU, L., CHIROIU, L., On the hysteresis operators, Proc. of the Romanian Academy, Series A: Mathematics, Physics, Technical Sciences, Information Science (in press).
KOPFOVÁ, J., Nonlinear semigroup methods in problems with hysteresis, Discrete and Continuous Dynamical Systems, Supplement, pp. 580–589, 2007.
VISINTIN, A., Hysteresis and semigroups, in: Models of Hysteresis (ed. A.Visintin), Longman, Harlow, 1993, pp. 192–206.
VISINTIN, A., Quasi-linear hyperbolic equations with hysteresis, Ann. Inst. H. Poincaré, Nonlinear Analysis, 19, pp. 451–476, 2002.
VISINTIN, A., Differential Models of Hysteresis, Springer-Verlag, Berlin, 1995.
VISINTIN, A., Homogenixation of some models of hysteresis, Physica B, 403, pp. 245–249, 2008.
KOPFOVÁ, J., Entropy condition for a quasilinear hyberbolic equation with hysteresis, Differential and Integral Equations, 18, 4, pp. 451–467, 2004.
CHARALAMPAKIS, A.E., KOUMOUSIS, V.K., A Bouc-Wen model compatible with plasticity postulates, Journal of Sound and Vibration, 322, pp. 954–968, 2009.
PREDA, V., IONESCU, M.F., CHIROIU, V., SIRETEANU, T., A Preisach model for the analysis of the hysteretic phenomena, Rev. Roum. Sci. Techn. – Méc. Appl., 55, 3, 2010.
GLIOZZI, A.S., MUNTEANU, L., SIRETEANU, T., CHIROIU, V., An identification problem from input-output data, Rev. Roum. Sci. Techn. – Méc. Appl., 55, 3, 2010.
MARINOSCHI, G., The diffusive form of Richard’s equation with hysteresis, Nonlinear Analysis: Real World Applications, 9, pp. 518–535, 2008.
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