References
M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov,Theory of Waves [in Russian], Nauka, Moscow (1990).
M. I. Rabinovich and D. I. Trubetskov,Introduction to Oscillation and Wave Theory [in Russian], Nauka, Moscow (1984).
Ya Ya Rushchitskii,Elements of the Theory of Mixtures [in Russian], Naukova Dumka, Kiev (1991).
Ya Ya. Rushchitskii, “Simple Riemann waves in hyperelastic bodies,”Dop. Natsion. Akad. Nauk Ukr., No. 10, 56–58 (1993).
Ya. Ya Rushchitskii, “Simple waves in quadratically nonlinear hyperelastic materials,”Prikl. Mekh.,30, No. 8, 35–41 (1994).
Ya. Ya. Rushchitskii, “Three-wave interaction and generation of a second harmonic in singlephase hyperelastic media,”Prikl. Mekh.,32, No. 7, 38–45 (1996).
Ya. Ya Rushchitskii, “On simple waves in solid mixtures,”Prikl. Mekh.,32, No. 9, 31–39 (1996).
Ya Ya Rushchitskii, “Nonlinear waves in solid mixtures (review),”Prikl. Mekh.,33, No. 1, 3–38 (1996).
Ya. Ya Rushchitskii, A. P. Kovalenko, and S. I. Tsutpal, “Distortion of a simple bell-shape wave in its propagation in a dual-phase material,”Dop. Natsion. Akad. Nauk Ukr., No. 8, 63–66 (1996).
L. I. Sedov,Continuum Mechanics [in Russian], in two volumes, Vol. 2, Nauka, Moscow (1970).
S. I. Tsurpal, “Solitaiy simple plane bell-shape waves in composite materials,” Author’s abstract of dissertation for Candidate of physical and mathematical sciences, Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev (1996).
M. J. Ablowitz and H. Segur,Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981).
E. Janke, F. Emde, and F. Losch,Tafeln Hoherer Funktionen, B. G. Teubner Verlagsgesellschaft, Stuttgart (1960).
J. Kampe de Feriet, R. Campbell, G. Petiau, and T. Vogel,Fonctions de la Physique Mathematique, Centre National de la Recherche Scientitique, Paris (1957).
J. Lighthill,Waves in Fluids, Cambridge University Press, Cambridge-London (1978).
B. Riemann, “Uber die fortpflanzung ebener Luftwellen von endlichen Schwingungsweite. Abhandfungen der Konigischen Gesellschaft der Wissenschaften zu Gottingen,” No. 8, (1860), in Bernhards Riemann’s Gesammelte Mathematische Werke und Wissenschaftlicher Nachlass, 2nd Auflage, Teubner Verlag, Leipzig (1892), in: B. Riemann.Gesammelte Matematische Werk, Wissenschafticher Nachlass und Nachtrage, Collected Papers, Springer Verlag/Teubner Verlagsgesellschaft, Berlin-Leipzig (1990).
J. J. Rushchitsky, “Simple plane waves in hyperelastic solids,” in:Abstract Book of Second European Solid Mechanics Conference. Section: Vibration, Waves, and Impacts, Section 1, School of Architecture of the University of Genoa, Genoa, Italy (1994).
J. J. Rushchitsky, “Phenomena of abreak down instability and parametric amplification of waves in dual-phase materials,” in:Abstracts of the Thirty-First Solid Mechanics Conference-SolMech ’96, Olszty n-Mierki, Poland (1996), pp. 211 -212.
J. J. Rushchitsky, “New solitary waves and their interaction in solid mixtures (granular composites),”ZAMM, 78, No. 2, 695–696 (1998).
M. Schubert and B. Wilhelmi,Einfuhrung in die Nichtineare Optik, Teil 1. Klassische Beschreibung, BSB B. G. Teubner Verlaggesellschaft, Leipzig, (1971).
J. Whitham,Linear And Nonlinear Waves. Wiley Interscience, New York (1974).
A. Yariv,Quantum Electronics, John Wiley and Sons, Inc., New York-London (1967).
Author information
Authors and Affiliations
Additional information
Translated from Prikladnaya Mekhanika, Vol. 34, No. 11, pp. 23–31, November, 1998.
Rights and permissions
About this article
Cite this article
Rushchitskii, Y.Y. On the interaction between solitary waves in solid mixtures. Int Appl Mech 34, 1086–1093 (1998). https://doi.org/10.1007/BF02700895
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02700895