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References
Askar, A., (1985), Lattice Dynamical Foundations of Continuum Theories. (Singapore: World Scientific).
Berezovski, A., Engelbrecht, J., and Maugin, G. A., (2003), Numerical simulation of two-dimensional wave propagation in functionally graded materials. Eur. J. Mech. Solids, 22, 2, 257-265.
Brillouin, L., (1953), Wave Propagation in Periodic Structures. (Toronto and London: Dover).
Capriz, G., (1989), Continua with Microstructure. (New York: Springer).
Christiansen, P. L., Muto, V., and Rionero, S., (1992), Solitary wave solution to a system of Boussinesq-like equations. Chaos Solitons Fractals, 2, 45-50.
Engelbrecht, J., (1983), Nonlinear Wave Processes of Deformation in Solids, (Boston: Pitman).
Engelbrecht, J., (1997), Nonlinear Wave Dynamics. Complexity and Simplicity, (Dordrecht: Kluwer).
Engelbrecht, J. and Pastrone, F., (2003), Waves in microstructured solids with strong nonlinearities in microscale. Proc. Estonian Acad. Sci. Phys. Math., 52, 12-20.
Engelbrecht, J., Berezovski, A., Pastrone, F., and Braun, M., (2004), Waves in microstructured materials and dispersion. Phil. Mag., 85, Nos 33-35, 4127-4141.
Engelbrecht, J., Cermelli, P., and Pastrone, F., (1999), Wave hierarchy in microstructured solids. Geometry, Continua and Microstructure, edited by G. A. Maugin (Paris: Hermann Publ.), pp. 99-111.
Eringen, A. C., (1966), Linear theory of micropolar elasticity. J. Math. Mech., 15, 909-923.
Eringen, A. C., (1999), Microcontinuum Field Theories. I Foundations and Solids. (New York: Springer).
Erofeyev, V. I., (2003), Wave Processes in Solids with Microstructure. (Singapore: World Scientific).
Janno, J. and Engelbrecht, J., (2005), Solitary waves in nonlinear microstructured materials, J. Phys. A: Math. Gen. 38, 5159-5172.
Maugin, G. A., (1990), Internal variables and dissipative structures. J. Nonequilib. Thermodyn., 15, 173-192.
Maugin, G. A., (1993), Material Inhomogeneities in Elasticity. (London: Chapman & Hall).
Maugin, G. A., (1999), Nonlinear Waves in Elastic Crystals. (Oxford: Oxford University Press).
Maugin, G. A. and Muschik W., (1994), Thermodynamics with internal variables. J. Nonequilib. Thermodyn. 19, 217-249 (Part I), 250-289 (Part II).
Mindlin, R. D., (1964), Micro-structure in linear elasticity. Arch. Rat. Mech. Anal., 16, 51-78.
Pastrone, F., (2003), Waves in solids with vectorial microstructure. Proc. Estonian Acad. Sci., 52, 1, 21-29.
Porubov, A. V., (2003), Amplification of Nonlinear Strain Waves in Solids. (Singapore: World Scientific).
Samsonov, A., (2001), Strain Solutons in Solids and How to Construct Them. (London: Chapman & Hall/CRC).
Santosa, F. and Symes W. W., (1991), A dispersive effective medium for wave propagation in periodic composites. SIAM J. Appl. Math., 51, 984-1005.
Wang, Z.-P. and Sun, C. T., (2002), Modeling micro-inertia in heterogeneous materials under dynamic loading. Wave Motion, 36, 473-485.
Whitham, G. B., (1974), Linear and Nonlinear Waves. (New York: Wiley).
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Engelbrecht, J., Pastrone, F., Braun, M., Berezovski, A. (2006). Hierarchies of Waves in Nonclassical Materials. In: Delsanto, P.P. (eds) Universality of Nonclassical Nonlinearity. Springer, New York, NY. https://doi.org/10.1007/978-0-387-35851-2_3
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DOI: https://doi.org/10.1007/978-0-387-35851-2_3
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