Extension of the microstructural theory of two-phase mixtures to composite materials

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M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov,The Theory of Waves [in Russian], Nauka, Moscow (1990).

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A. N. Guz',The Stability of Elastic Bodies Subject to Finite Strains [in Russian], Naukova Dumka, Kiev (1973).

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V. A. Krasil'nikov and V. V. Krylov,Introduction to Physical Acoustics [in Russian], Nauka, Moscow (1986).

B. P. Maslov, Ya. Ya. Rushchitskii, and A. P. Kovalenko, “Complete sets of physical constants for the nonlinear microstructural theory of two-phase elastic, mixtures evaluated for some structural granulated composites,”Prikl. Mekh.,32, No. 11, 41–49 (1996).

A. N. Guz (ed.),The Mechanics of Composites and Structural Elements [in Russian], in three vols., Naukova Dumka, Kiev (1982).

A. N. Guz' (ed.),The Mechanics of Composites [in Russian], in 12 vols., Naukova Dumka, Kiev (1993–2000).

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B. E. Pobedrya and V. I. Gorbachev, “Static problems of elastic composites,”Vest. Mosk. Univ., Ser. Mat. Mekh., No. 5, 101–110 (1977).

B. E. Pobedrya, “The theory of viscoelasticity of composites” in:Mechanics of Composites [in Russian], Vol. 3 (1979), pp. 414–423.

B. E. Pobedrya,Numerical Methods in the Theory of Elasticity and Plasticity [in Russian], Izd. Mosk. Univ. (1981).

M. I. Rabinovich and D. I. Trubetskov,Introduction to the Theory of Vibrations and Waves [in Russian], Nauka, Moscow (1984).

Kh. A. Rakhmatulin, Ya. U. Saatov, I. G. Filippov, and T. U. Artykov,Waves in Two-Component Media [in Russian], Fan, Tashkent (1974).

Ya. Ya. Rushchitskii, “General solutions in the theory of a mixture of two elastic media,” in:Abstracts of Papers Read at the 4th Polish-Soviet Symp. on Nonclassical Problems of Mechanics [in Russian], Warsaw (1973), p. 21.

Ya. Ya. Rushchitskii, “The use of the Papkovich-Neiber solution in the theory of a mixture of two solids,”Prikl. Mekh. 9, No. 9, 17–23 (1973).

Ya. Ya. Rushchitskii, “A plane problem of the theory of a mixture of two solids,”Prikl. Mekh.,10, No. 2, 52–61 (1974).

Ya. Ya. Rushchitskii, “Torsional waves in a cylinder made from a composite material,”Prikl. Mekh.,12, No. 5, 18–23 (1976).

Ya. Ya. Rushchitskii, “One case of wave propagation in mixtures of elastic materials,”Prikl. Mekh.,14, No. 1, 25–33 (1978).

Ya. Ya. Rushchitskii, “Laws of wave propagation in mixtures of elastic materials,” in:Abstracts of Papers Read at the 6th Polish-Soviet Symp. on Nonclassical Problems of Mechanics [in Russian], Warsaw (1978), p. 18.

Ya. Ya. Rushchitskii, “Using experimental dispersion curves to determine the physical constants of the theory of a mixture of elastic materials,”Prikl. Mekh.,15, No. 6, 26–32 (1979).

Ya. Ya. Rushchitskii, “Analysis of the boundary effect in a linear mixture of elastic media,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 4, 52–55 (1980).

Ya. Ya. Rushchitskii, “Applicability of the linear theory of mixtures,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 6, 58–62 (1980).

Ya. Ya. Rushchitskii, “General representations for the solutions of the equations of the linear theory of a mixture of elastic media,”Prikl. Mekh.,16, No. 7, 3–11 (1980).

Ya. Ya. Rushchitskii, “Variation principles of the linearized theory of mixtures,”Prikl. Mekh.,16, No. 10, 134–136 (1980).

Ya. Ya. Rushchitskii, “Phase velocities, group velocities, and velocities of movement of the energy of a plane wave in a mixture of elastic materials,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 8, 50–52 (1981).

Ya. Ya. Rushchitskii, “The torsion of a direct beam made from a mixture of elastic materials,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 9, 51–54 (1981).

Ya. Ya. Rushchitskii, “Physical constants in the theory of mixtures,”Prikh. Mekh.,17, No. 11 134–136 (1981).

Ya. Ya. Rushchitskii, “The stability of the equilibrium state in the theory of mixtures,”Prikl. Mekh.,17, No. 12, 51–58 (1981).

Ya. Ya. Rushchitskii, “Propagation of plane viscoelastic waves in a mixture of elastic materials,”Prikl. Mekh.,18, No. 1, 93–99 (1982).

Ya. Ya. Rushchitskii, “Study of the basic problems of the mechanics of a mixture of elastic media,”Author's Abstract and Thesis of Doctoral Dissertation [in Russian], Inst. Mekh. Akad. Nauk Ukrainy, Kiev, (1982).

Ya. Ya. Rushchitskii, “Inherent instability in mixtures,”Prikl. Mekh.,18, No. 12, 48–53 (1982).

Ya. Ya. Rushchitskii, “Description of wave phenomena in materials with a microstructure using the theory of mixtures”, in:Abstracts of Papers Read at the 5th National Congress on Theoretical and Applied Mechanics [in Russian], Varna (1985), p. 93.

Ya. Ya. Rushchitskii, “A new microstructural model of the deformation of materials”Trans. Lavrentiev's Readings on Mathematics, Mechanics, and Physics [in Russian], Naukova Dumka, Kiev (1985), pp. 184–186.

Ya. Ya. Rushchitskii, “Phenomenological description of interaction in the linear theory of a mixture of elastic media,”Prikl. Mekh.,22, No. 5, 90–95 (1986).

Ya. Ya. Rushchitskii, “The validity of a mixture model in the mechanics of composites,” in:Abstracts of Papers Read at the 6th All-Union Congress on Theoretical and Applied Mechanics [in Russian], Tashkent (1986), p. 54.

Ya. Ya. Rushchitskii, “Stability analysis in the mechanics of composites using the theory of mixtures,” in:Abstracts of Papers Read at the All-Union Symp. on Stability in the Mechanics of a Deformable Solid [in Russian], Kalinin-Tver' (1986), pp. 195–196.

Ya. Ya. Rushchitskii, “Microstructural theories in the mechanics of composites,” in:Abstracts of Papers Read at the 7th Polish-Soviet Symp. on Nonclassical Problems of Mechanics [in Russian], Warsaw-Yablonna (1987), p. 33.

Ya. Ya. Rushchitskii, “Microstructural theories in the mechanics of composites,” in:Advances in the Machine Industry: Composition Materials. Int. Center Sci. Eng. Inf., A. A. Blagonravov Inst. Mech. Eng., MTsNTI, Moscow (1987), pp. 83–98.

Ya. Ya. Rushchitskii, “A nonlinear wave in a two-phase material,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 1, 49–52 (1990).

Ya. Ya. Rushchitskii, “A plane nonlinear wave in a two-phase material,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 2, 45–47 (1990).

Ya. Ya. Rushchitskii, “Element of the Theory of Mixtures [in Russian], Naukova Dumka, Kiev (1991).

Ya. Ya. Rushchitskii, “Interaction of elastic waves in a two-phase material,”Prikl. Mekh.,28, No. 5, 13–21 (1992).

Ya. Ya. Rushchitskii, “A Continual Model of a Mixture in the Mechanics of Laminates, Chapter 9 of the monographThe Dynamics and Stability of Laminated Composites [in Russan], Naukova Dumka, Kiev (1993), pp. 228–263.

Ya. Ya. Rushchitskii, “Propagation of Long Waves in Composites (a Continual Theory of the First Order), Chapter 10, Vol. 2 of the 12-volume seriesMechanics of Composites [in Russian], Naukova Dumka, Kiev (1993–2002), pp. 377–405.

Ya. Ya. Rushchitskii, “Interaction of compression and shear waves in a composite material with nonlinearly elastic components in the microstructure,”Prikl. Mekh.,29, No. 4, 18–26 (1993).

Ya. Ya. Rushchitskii, “Riemann's simple waves in hyperelastic bodies,”Dop. Akad. Nauk Ukrainy, No. 10, 56–58 (1993).

Ya. Ya. Rushchitskii, “Nonlinear plane waves in an orthotropic body,”Dop. Akad. Nauk Ukrainy, No. 12, 60–62 (1993).

Ya. Ya. Rushchitskii, “The resonance interaction of nonlinear waves in two-phase mixtures,”Prikl. Mekh.,30, No. 5, 32–41 (1994).

Ya. Ya. Rushchitskii, “Simple waves in quadratically nonlinear hyperelastic materials,”Prikl. Mekh.,30, No. 8, 35–41 (1994).

Ya. Ya. Rushchitskii, “Analysis of wave interaction in two-phase materials within the framework of the microstructural theory of mixtures,” in:Abstracts of Papers Read at the Int. Sci. Colloq. on Nonlinear Dynamics of Solids with a Microstructure [in Russian], Nizhnyi Novgorod (1995), pp. 21–22.

Ya. Ya. Rushchitskii, “A model of a solid mixture for granulated piezoelectric materials,” in:Abstracts of Papers read at the 4th Int. Conf. on the Mechanics of Inhomogeneous Structures [in Ukrainian], L'vov-Ternopol' (1995), p. 89.

Ya. Ya. Rushchitskii, “Waves and the direct piezoelectric effect in two-phase piezoelectrics,”Prikl. Mekh.,31, No. 10, 42–48 (1995).

Ya. Ya. Rushchitskii, “Three-wave interaction and generation of the second harmonic in single-phase and two-phase hyperelastic media,”Prikl. Mekh.,32, No. 7, 38–45 (1996).

Ya. Ya. Rushchitskii, “Simple waves in solid mixtures,”Prikl. Mekh.,32, No. 9, 31–39 (1996).

Ya. Ya. Rushchitskii, “Simple waves,”Dop. Akad. Nauk Ukrainy, No. 12, 55–60 (1996).

Ya. Ya. Rushchitskii, “Nonlinear waves in solid mixtures (review),”Prikl. Mekh.,33, No. 1, 3–39 (1997).

Ya. Ya. Rushchitskii, “The interaction of simple waves in solid mixtures,”Dop. NAN Ukrainy, No. 3, 64–70 (1999).

Ya. Ya. Rushchitskii, “Unconventional ordered pairs of thermodynamic parameters: from Podstrigach's theory of diffusion elasticity to the Bedford-Drumheller theory of mixtures,”Mat. Metody Fiz.-Mekh. Polya, L'vov,41, No. 3, 117–120 (1998–1999).

Ya. Ya. Rushchitskii and A. A. Abduganiev, “A theory of mixtures based on the Bedford-Drumheller model for a saturated porous medium,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 12, 38–39 (1989).

Ya. Ya. Rushchitskii and A. A. Abduganiev, “Two unconventional concepts of the mechanics of a multiphase mixture,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 11, 61–64 (1992).

Ya. Ya. Rushchitskii and A. A. Abduganiev, “A new class of linearized problems depending on the parameters of the initial state,”Prikl. Mekh.,30, No. 7, 9–16 (1994).

Ya. Ya. Rushchitskii and V. A. Belyi, “Existence of one type of combination dissipation of sound by sound in a two-phase solid,”Dop. NAN Ukrainy, No. 10, 58–63 (1994).

Ya. Ya. Rushchitskii and V. A. Belyi, “The decomposing instability of triplets in a hyperelastic two-phase medium,”Dop. NAN Ukrainy, No. 11, 57–63 (1996).

Ya. Ya. Rushchitskii, A. P. Kovalenko, and E. V. Savel'eva, “Self-generation of lateral waves in hyperelastic media,”Prikl. Mekh.,32, No. 5, 30–38 (1996).

Ya. Ya. Rushchitskii, A. P. Kovalenko, and S. I. Tsurpal, “The distortion of a simple bell-shaped wave propagating in a two-phase material,”Dop. NAN Ukrainy, No. 8, 63–66 (1996).

Ya. Ya. Rushchitskii, A. P. Kovalenko, V. A. Belyi, and S. I. Tsurpal, “The distortion of a simple longitudinal wave in an inhomogeneous solid,”Prikl. Mekh.,33, No. 9, 15–23 (1997).

Ya. Ya. Rushchitskii and I. A. Ostrakov, “Generation of new harmonics of nonlinear elastic waves in a composite material,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 10, 63–66 (1991).

Ya. Ya. Rushchitskii and I. A. Ostrakov, “The distortion of a plane harmonic wave propagating in a composite material,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 11, 51–54 (1991).

Ya. Ya. Rushchitskii and S. O. Rushchitskaya, “Spherical waves in the theory of mixtures,”Prikl. Mekh.,12, No. 6, 63–69 (1976).

Ya. Ya. Rushchitskii and S. O. Rushchitskaya, “Features of solutions in the theory of mixtures,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 6, 531–534 (1976).

Ya. Ya. Rushchitskii and S. O. Rushchitskaya, “The generalized solution of one differential problem of mechanics,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 7, 632–636 (1974).

Ya. Ya. Rushchitskii and S. O. Rushchitskaya, “The Sommerfeld conditions in the theory of mixtures,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 8, 730–733 (1976).

Ya. Ya. Rushchitskii and S. O. Rushchitskaya, “Saint Venant's principle in the theory of a mixture of elastic media,”Prikl. Mekh.,13, No. 6, 12–17 (1977).

Ya. Ya. Rushchitskii and S. O. Rushchitskaya, “Description of features of the wave phenomena in composite materials,”Mekh. Komp. Mater., No. 5, 894–900 (1996).

Ya. Ya. Rushchitskii and E. V. Savel'eva, “The evolution of a harmonic wave propagating in a two-phase material,”Prikl. Mekh.,28, No. 9, 42–46 (1992).

Ya. Ya. Rushchitskii and I. M. Khotenko, “Linear waves in two-phase piezoelectric materials,”Dop. NAN Ukrainy, No. 3, 41–43 (1995).

Ya. Ya. Rushchitskii and B. M. Khotenko, “Creation of a quadratically nonlinear theory of wave propagation in two-phase piezoelectric powders,”Dop. NAN Ukrainy, No. 9, 61–67 (1998).

Ya. Ya. Rushchitskii and B. M. Khotenko, “Nonlinear plane harmonic waves in two-phase piezoelectric powders,”Dop. NAN Ukrainy, No. 10, 60–66 (1998).

Ya. Ya. Rushchitskii and S. I. Tsurpal, “Generation of a new simple wave by a longitudinal simple wave in a hyperelastic two-phase medium,”Dop. NAN Ukrainy, No. 7, 56–60 (1996).

Ya. Ya. Rushchitskii and S. B. Tsurpal,Waves in Materials with a Microstructure [in Russian], Inst, Mekh. NANU, Kiev (1998).

Ya. Ya. Rushchitskii and B. B. Érgashev, “Calculation of the shear-interaction factor for isotropic structural materials filled with microspheres,”Prikl. Mekh.,23, No. 9, 52–58 (1987).

Ya. Ya. Rushchitskii and B. B. Érgashev, “The theory of effective moduli of composite materials filled with hollow microspheres,”Prikl. Mekh.,23, No. 11, 17–21 (1987).

Ya. Ya. Rushchitskii and B. B. Érgashev, “Theoretical analysis of nonstationary effects in a massive specimen made from fibrous composite and subject to a short-term harmonic impulse,”Prikl. Mekh.,23, No. 12, 81–86 (1987).

Ya. Ya. Rushchitskii and B. B. Érgashev, “The vibrations of a hollow cylinder made from a composite and subject to impulse internal pressure,”Prikl. Mekh.,25, No. 7, 30–37 (1989).

Ya. Ya. Rushchitskii and B. B. Érgashev, “The shear-interaction coefficient for granulated composites filled with solid microspheres,”Prikl. Mekh.,25, No. 9, 126–128 (1989).

Ya. Ya. Rushchitskii and B. B. Érgashev, “The relations for calculation of the physical constants of the isotropic theory of mixtures,”Prikl. Mekh.,25, No. 11, 62–66 (1989).

Ya. Ya. Rushchitskii and B. B. Érgashev, “Some features of the natural vibrations of a mixture,”Prikl. Mekh.,26, No. 1, 16–22 (1990).

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G. N. Savin and Ya. Ya. Rushchitskii, “Surface waves in the theory of a mixture of elastic materials,”Abstracts of Papers Read at the 4th All-Union Symp. on Propagation of Elastic and Elastoplastic Waves [in Russian], Bishkek (1976), pp. 118–119.

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J. J. Rushchitsky, “The microstructural theory of mixtures”, in:Annotations of Papers Read at IUTAM/ICM Symp. on Loading, Failure, and Fracture of Anisotropic Solids, Antony Sawczuk Memoriam, Grenoble, France (1987), p. 35.

J. J. Rushchitsky, “Microstructural theory of the mixture: conception, main mechanical effects, features of elastic and viscoelastic waves, practicability to composite materials”,Proc. Intern. Congress on Appl. Mechanics, Vol. 2, Beijing, China (1989), pp. 42–46.

J. J. Rushchitsky, “Nonlinear interaction of elastic waves in composite materials,” in:Abstracts of Lectures Read at the Yugoslav Conf. on Nonlinear Deterministic and Stochastic Processes in Dynamical Systems with Applications, University of Nis, Yugoslavia, Nis (1991), p. 57.

J. J. Rushchitsky, “Nonlinear elastic waves in solids with inner microstructure, new effects and features,” in:Annotations of Lectures Read at the 15th Int. Symp. on Vibrations in Physical Systems, Poznan (1992), p. 140.

J. J. Rushchitsky, “Nonlinear elastic waves in isotropic multi-phase materials (composites): interaction, second harmonics generation, new complex waves, evolution, distortion, blow up, triplets”, inAbstracts of Papers Read at the IUTAM Symp. on Nonlinear Waves in Solids, Victoria, British Columbia, Canada (1993), p. 43.

J. J. Rushchitsky, “Analytical investigation of wave triplets in a multi-phase medium”, in:Abstracts of Papers Read at the 1st European and 13th Intern. Conf. on Nonlinear Vibrations, Harburg, Germany (1993), p. 138.

J. J. Rushchitsky, “The combinational scattering of sound on sound in multi-phase solids”, in:Annotations of Lectures Read at the 15th Intern. Symp. on Vibrations in Physical Systems, Poznan, Poland (1994), p. 124.

J. J. Rushchitsky, “Simple plane waves in hyperelastic solids”, in:Abstract Book 2nd European Solid Mechanics Conference, Section:Vibration, Waves and Impacts, S. I, School of Architecture of the University of Genoa, Genoa, Italy (1994).

J. J. Rushchitsky, “Lax-Nelson problem on the direct piezoelectric effect in two-phase materials”, in:Abstracts of Papers Read at the 3rd Intern. Congress on Industrial and Applied Mathematics (ICIAM 95), Hamburg, Germany (1995), p. 465.

J. J. Rushchitsky, “Interaction of elastic waves in an isotropic multi-phase materials”,J. Theor. Appl. Mech., Bulgarian Academy of Sciences, No. 3-4, 82–93 (1994–1995).

J. J. Rushchitsky, “Wave triplets in two-phase composites,”Mech. Composite Mater. No. 5, 660–670 (1995).

J. J. Rushchitsky, “Lax-Nelson problem on the direct piezoelectric effect in two-phase materials”, in:Zeitschrift für Angewandte Mathematik und Mechanik, Special issue for lectures the ICIAM/GAMM 95,76, Supplement 2 (1996), pp. 663–664.

J. J. Rushchitsky, “New dispersive simple wave (new partial solution) in nonlinear solid mixtures”, in:Abstracts of Papers Read at the 2nd European Conf. on Nonlinear Vibrations, Prague, Czech Republic (1996), p. 413.

J. J. Rushchitsky, “Phenomena of a break-down instability and parametric amplification of waves in two-phase materials,” in:Abstracts of Papers Read at the 31st Solid Mechanics Conf. SolMech'96, Olsztyn-Mierki, Poland (1996), pp. 211–212.

J. J. Rushchitsky, “New properties of transverse waves in quadratic nonlinear elastic materials (nonclassic results in classic theory),” in:Annotations of Lectures Read at the 15th Int. Symp. on Vibrations in Physical Systems, Poznan, Poland (1996), pp. 228–229.

J. J. Rushchitsky, “Notes on simple wave energy”,Technicka Mechanika—Engineering Mechanics,4, No. 6, 327–334 (1997).

J. J. Rushchitsky, “New solitary waves and their interaction in solid mixtures (granular composites)”,Zeitschrift für Angewandte Mathematik und Mechanik, Special issue for lectures the GAMM 97,78, Supplement 1 (1998), pp. 626–627.

J. J. Rushchitsky, “New dispersive simple wave (new partial solution) in nonlinear solid mixtures”, in:Proc. 2nd European Nonlinear Oscillations Conference,3, Prague, Czech Republic (1997), pp. 141–144.

J. J. Rushchitsky, “About energy propagation velocity of classic, dispersive, and simple waves in materials”, in:Annotation of Lectures Read at the 18th Symp. on Vibrations in Physical Systems, Poznan, Poland (1998), pp. 302–303.

J. J. Rushchitsky, “Nonlinear shear piezoelastic waves in piezoelectric powders”, in:Abstracts of Papers Read at the GAMM 98 Jahrestagung, Bremen, Germany (1998), pp. 117.

J. J. Rushchitsky, “Interaction of solitary waves in two-phase materials”,Int. Appl. Mech.,34, No. 11, 1134–1139 (1998).

J. J. Rushchitsky, “On classification of elastic waves”,Int. Appl. Mech.,35, No. 11, pp. 1104–1110 (1999).

J. J. Rushchitsky, “Interaction of waves in solid mixtures”,Appl. Mech. Rev.,52, No. 2, 35–74 (1999).

J. J. Rushchitsky, “Nonlinear interaction of elastic solitary waves in materials”, in:Abstracts of Papers Read at the 3rd European Conf. on Nonlinear Oscillations (August 8–12), Denmark, Copenhagen (Lyngby) (1999), pp. 36–37.

J. J. Rushchitsky, “Interaction of solitary and harmonic waves in materials with the microstructure”, in:Abstracts of Papers Read at the 27th Int. Conf.-School on Analysis and Synthesis of Nonlinear Mechanical Oscillating Systems (September, 1–10) St-Petersburg, Russia (1999).

J. J. Rushchitsky, “About the transition of the continuous wave into the shock wave during its propagation in a composite material”, in:Proc. EUROMECH 400 Colloq. on Impact and Damage Tolerance Modeling of Composite Materials and Structures (September, 27–29), London, United Kingdom (1999), pp. 154–157.

J. J. Rushchitsky, and I. M. Khotenko, “Nonlinear plane waves in piezoelectric powders”,Annotations of Lectures Read at the 18th Symp. on Vibrations in Physical Systems, Poznan, Poland (1998), pp. 230–231.

J. J. Rushchitsky and I. M. Khotenko, “On nonlinear waves in two-phase piezopowders”,Int. Appl. Mech.,34, No. 8, 750–755 (1998).

J. J. Rushchitsky and S. O. Rushchitska, “An interaction of simple solitary waves with profiles in the form of Chebyshov-Hermite, Mathieu, and Whittaker functions in media with the microstructure”,Proc. Int. Symp. TRECOP'98 on Trends in Continuum Physics (D. Maruszewski, W. Muschik, and A. Radowicz, editors), World Scientific, Singapore-London (1999), pp. 392–300.

J. J. Rushchitsky and S. O. Rushchitska, “On simple waves with profiles in the form of some special functions—Chebyshov-Hermite, Mathieu, and Whittaker—in two-phase media”, in:Proc. Mark Krein Int. Conf. on Series-Operator Theory, Advances and Applications, Vol. 117,Differential Operators and Related Topics (R. Kaashoek, E. Adamian, M. Gorbachuk, and E. Popov, editors), Kluwer, Amsterdam (2000), pp. 313–322.

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