Evolution of wave fields in block relaxing media
DOI:
https://doi.org/10.15407/dopovidi2015.01.080Keywords:
Burgers' equation, evolution, geoblock, stressAbstract
A continual model for block media is studied. It takes the discontinuities of velocities and stresses between structural elements of media into account. Using the methods of the reductive theory of perturbations, the (1 + 2) second order amplitude equation of the Burgers type is constructed. Kink- like wave and self-similar solutions of the amplitude equation are derived.Downloads
References
Sadovskii M. A. Vest. AN USSR, 1986, 8: 3–11 (in Russian).
Vakhnenko V. A., Danilenko V. A., Kulich V. V. Elements of the theory of self-organization and nonlinear wave processes in natural environments with the structure, Kyiv, 1991 (in Russian).
Danylenko V. A., Danevych T. B., Makarenko O. S., Skurativskyi S. I., Vladimirov V. A. Self-organization in nonlocal non-equilibrium media, Kyiv: Subbotin Inst. of Geophysics of the NAS of Ukraine, 2011.
Filippov B. V., Khantuleva T. A. Boundary problems nonlocal hydrodynamics, Leningrad: Iz-vo Leningr. Univ., 1984 (in Russian).
Danylenko V. A. Reports of the National Academy of Sciences of Ukraine, 1992, 2: 86–89 (in Ukrainian).
Danylenko V. A., Skurativskii S. I. Reports of the National Academy of Sciences of Ukraine, 2011, 9: 90–97 (in Ukrainian).
Dodd R., J. Elbek., J. Gibbon et al. Solitons and nonlinear wave equations. Moscow: Mir, 1988 (in Russian).
Danylenko V. A., Danevych T. B. Reports of the National Academy of Sciences of Ukraine, 2004, 3: 110-114 (in Ukrainian).
Zaitsev V. F., Polianyn A. D. Spravochnyk po obyknovennym dyfferentsyal'nym uravnenyiam, Moscow: Fizmalit., 2001 (in Russian).
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