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... Stegun, I. A. (Editors),Handbook of Mathematical Functions with Formulas, ... Arscott, F., Periodic Differential Equations, Macmillan (Pergamon), New York, 1964. .... Haberman, R.,Elementary Applied Partial Differential Equations with Fourier ...
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REFERENCES Abramowitz, M. and Stegun, I. A. (Editors), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards Applied Mathematics, Washington, 1964. Acrivos, A., A note of the rate of heat or mass transfer from a small sphere freely suspended in linear shear field, J. Fluid Mech., Vol. 98, No. 2, pp. 299–304, 1980. Aksenov, A. V., Linear differential relations between solutions of the equations of Euler–Poisson– Darboux class, Mechanics of Solids, Vol. 36, No. 1, pp. 11–15, 2001. Akulenko, L. D. and Nesterov, S. V., Determination of the frequencies and forms of oscillations of non-uniform distributed systems with boundary conditions of the third kind, Appl. Math. Mech. (PMM), Vol. 61, No. 4, p. 531–538, 1997. Akulenko, L. D. and Nesterov, S. V., Vibration of an nonhomogeneous membrane, Mechanics of Solids, Vol. 34, No. 6, pp. 112–121, 1999. Akulenko, L. D. and Nesterov, S. V., Free vibrations of a homogeneous elliptic membrane, Mechanics of Solids, Vol. 35, No. 1, pp. 153–162, 2000. Akulenko, L. D., Nesterov, S. V., and Popov, A. L., Natural frequencies of an elliptic plate with clamped edge, Mechanics of Solids, Vol. 36, No. 1, pp. 143–148, 2001. Andreev, V. K., Kaptsov, O. V., Pukhnachov, V. V., and Rodionov, A. A., Applications of GroupTheoretical Methods in Hydrodynamics, Nauka, Moscow, 1994. (English translation: Kluwer, Dordrecht, 1999.) Appell, P., Trait´e de M´ecanique Rationnelle, T. 1: Statique. Dinamyque du Point (Ed. 6), GauthierVillars, Paris, 1953. Arscott, F., Periodic Differential Equations, Macmillan (Pergamon), New York, 1964. Arscott, F., The Whittaker–Hill equation and the wave equation in paraboloidal coordinates, Proc. Roy. Soc. Edinburg, Vol. A67, pp. 265–276, 1967. Babich, V. M., Kapilevich, M. B., Mikhlin, S. G., et al., Linear Equations of Mathematical Physics [in Russian], Nauka, Moscow, 1964. Batchelor, G. K., Mass transfer from a particle suspended in fluid with a steady linear ambient velocity distribution, J. Fluid Mech., Vol. 95, No. 2, pp. 369–400, 1979. Bateman, H. and Erd´elyi, A., Higher Transcendental Functions, Vol. 1 and Vol. 2, McGraw-Hill, New York, 1953. Bateman, H. and Erd´elyi, A., Higher Transcendental Functions, Vol. 3, McGraw-Hill, New York, 1955. Bateman, H. and Erd´elyi, A., Tables of Integral Transforms, Vol. 1 and Vol. 2, McGraw-Hill, New York, 1954. Belotserkovskii, O. M., and Oparin, A. A., Numerical Experiment in Turbulence, Nauka, Moscow, 2000. Beyer, W. H., CRC Standard Mathematical Tables and Formulae, CRC Press, Boca Raton, 1991. Bitsadze, A. V. and Kalinichenko, D. F., Collection of Problems on Mathematical Physics Equations [in Russian], Nauka, Moscow, 1985. Bolotin V. V. (Editor), Vibration in Engineering: a Handbook. Vol. 1. Vibration of Linear Systems [in Russian], Mashinostroenie, Moscow, 1978.

© 2002 by Chapman & Hall/CRC Page 769

770

REFERENCES

Borzykh, A. A. and Cherepanov, G. P., A plane problem of the theory of convective heat transfer and mass exchange, PMM [Applied Mathematics and Mechanics], Vol. 42, No. 5, pp. 848–855, 1978. Boyer, C., The maximal kinematical invariance group for an arbitrary potential, Helv. Phys. Acta, Vol. 47, pp. 589–605, 1974. Boyer, C., Lie theory and separation of variables for equation Œ> o + Ž 2  − (  t i 21 +  t ‘ 22 )  = 0, SIAM J. Math. Anal., Vol. 7, pp. 230–263, 1976. Bˆocher, M., Die Reihenentwickelungen der Potentialtheory, Leipzig, 1894. Brenner, H., Forced convection-heat and mass transfer at small Peclet numbers from particle of arbitrary shape, Chem. Eng. Sci., Vol. 18, No. 2, pp. 109–122, 1963. Brychkov, Yu. A. and Prudnikov, A. P., Integral Transforms of Generalized Functions, Gordon & Breach Sci. Publ., New York, 1989. Budak, B. M., Samarskii, A. A., and Tikhonov, A. N., Collection of Problems on Mathematical Physics [in Russian], Nauka, Moscow, 1980. Burde, G. I., The construction of special explicit solutions of the boundary-layer equations. Steady flows, Q. J. Mech. Appl. Math., Vol. 47, No. 2, pp. 247–260, 1994. Butkov, E., Mathematical Physics, Addison-Wesley, Reading, Mass., 1968. Butkovskiy, A. G., Characteristics of Systems with Distributed Parameters [in Russian], Nauka, Moscow, 1979. Butkovskiy, A. G., Green’s Functions and Transfer Functions Handbook, Halstead Press–John Wiley & Sons, New York, 1982. Carslaw, H. S. and Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, Oxford, 1984. Clarkson, P. A and Kruskal, M. D., New similarity reductions of the Boussinesq equation, J. Math. Phys., Vol. 30, No. 10, pp. 2201–2213, 1989. Colton, D., Partial Differential Equations. An Introduction, Random House, New York, 1988. Courant, R. and Hilbert, D., Methods of Mathematical Physics, Vol. 2, Wiley–Interscience Publ., New York, 1989. Crank, J., The Mathematics of Diffusion, Clarendon Press, Oxford, 1975. Davis, B., Integral Transforms and Their Applications, Springer-Verlag, New York, 1978. Davis, E. J., Exact solutions for a class of heat and mass transfer problems, Can. J. Chem. Eng., Vol. 51, No. 5, pp. 562–572, 1973. Deavours, C. A., An exact solution for the temperature distribution in parallel plate Poiseuille flow, Trans. ASME, J. Heat Transfer, Vol. 96, No. 4, 1974. Dezin, A. A., Partial Differential Equations. An Introduction to a General Theory of Linear Boundary Value Problems, Springer-Verlag, Berlin-New York, 1987. Ditkin, V. A. and Prudnikov, A. P., Integral Transforms and Operational Calculus, Pergamon Press, New York, 1965. Doyle, Ph. W., Separation of variables for scalar evolution equations in one space dimension, J. Phys. A: Math. Gen., Vol. 29, pp. 7581–7595, 1996. Doyle, Ph. W. and Vassiliou, P. J., Separation of variables for the 1-dimensional non-linear diffusion equation, Int. J. Non-Linear Mech., Vol. 33, No. 2, pp. 315–326, 1998. Elrick, D. E., Source functions for diffusion in uniform shear flows, Australian J. Phys., Vol. 15, No. 3, p. 283–288, 1962. Faddeev, L. D. (Editor), Mathematical Physics. Encyclopedia [in Russian], Bol’shaya Rossiiskaya Entsyklopediya, Moscow, 1998. Faminskii, A. V., On mixed problems for the Corteveg–de Vries equation with irregular boundary data, Doklady Mathematics, Vol. 59, No. 3, pp. 366–367, 1999.

© 2002 by Chapman & Hall/CRC Page 770

REFERENCES

771

Farlow, S. J., Partial Differential Equations for Scientists and Engineers, John Wiley & Sons, New York, 1982. Galaktionov, V. A., Invariant subspace and new explicit solutions to evolution equations with quadratic nonlinearities, Proc. Roy. Soc. Edinburgh, Vol. 125A, No. 2, pp. 225–448, 1995. Galaktionov, V. A. and Posashkov, S. A., On new exact solutions of parabolic equations with quadratic nonlinearities, Zh. Vych. Matem. i Mat. Fiziki, Vol. 29, No. 4, pp. 497–506, 1989. Galaktionov, V. A. and Posashkov, S. A., Exact solutions and invariant subspace for nonlinear gradient-diffusion equations, Zh. Vych. Matem. i Mat. Fiziki, Vol. 34, No. 3, pp. 374–383, 1994. Galaktionov, V. A., Posashkov, S. A., and Svirshchevskii, S. R., Generalized separation of variables for differential equations with polynomial right-hand sides, Dif. Uravneniya, Vol. 31, No. 2, pp. 253–261, 1995. Gel’fand, I. M. and Shilov, G. E., Distributions and Operations on Them [in Russian], Fizmatlit, Moscow, 1959. Gradshteyn, I. S. and Ryzhik, I. M., Tables of Integrals, Series, and Products, Academic Press, Orlando, 2000. ¨ Graetz, L., Uber die Warmeleitungsfa¨ higkeit von Fl¨ussigkeiten, Annln. Phys., Bd. 18, S. 79–84, 1883. Grundland, A. M. and Infeld, E., A family of nonlinear Klein–Gordon equations and their solutions, J. Math. Phys., Vol. 33, No. 7, pp. 2498–2503, 1992. Guenther, R. B. and Lee, J. W., Partial Differential Equations of Mathematical Physics and Integral Equations, Dover Publ., Mineola, 1996. Gupalo, Yu. P., Polyanin, A. D., and Ryazantsev, Yu. S., Mass Exchange of Reacting Particles with Flow [in Russian], Nauka, Moscow, 1985. Gupalo, Yu. P. and Ryazantsev, Yu. S., Mass and heat transfer from a sphere in a laminar flow, Chem. Eng. Sci., Vol. 27, pp. 61–68, 1972. Haberman, R., Elementary Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, Prentice-Hall, Englewood Cliffs, 1987. Hanna, J. R. and Rowland, J. H. Fourier Series, Transforms, and Boundary Value Problems, Wiley-Interscience Publ., New York, 1990. Happel, J. and Brenner, H., Low Reynolds Number Hydrodynamics, Prentice-Hall, Englewood Cliffs, 1965. H¨ormander, L., The Analysis of Linear Partial Differential Operators. II. Differential Operators with Constant Coefficients, Springer-Verlag, Berlin-New York, 1983. H¨ormander, L., The Analysis of Linear Partial Differential Operators. I. Distribution Theory and Fourier Analysis, Springer-Verlag, Berlin, 1990. Ibragimov N. H. (Editor), CRC Handbook of Lie Group to Differential Equations, Vol. 1, CRC Press, Boca Raton, 1994. Ignatovich, N. V., Invariant irreducible, partially invariant solutions of stationary boundary layer equations, Mat. Zametki, Vol. 53, No. 1, pp. 140–143, 1993. Ivanov, V. I., and Trubetskov, M. K., Handbook of Conformal Mapping with Computer-Aided Visualization, Boca Raton, CRC Press, 1994. John, F., Partial Differential Equations, Springer-Verlag, New York, 1982. Kalnins, E., On the separation of variables for the Laplace equation in two- and three-dimensional Minkowski space, SIAM J. Math. Anal., Hung., Vol. 6, pp. 340–373, 1975. Kalnins, E. and Miller, W. (Jr.), Lie theory and separation of variables, 5: The equations Œ> o +  s s = 0 and Œ> o +  s s − s ’ 2  = 0, J. Math. Phys., Vol. 15, pp. 1728–1737, 1974.

© 2002 by Chapman & Hall/CRC Page 771

772

REFERENCES

Kalnins, E. and Miller, W. (Jr.), Lie theory and separation of variables, 8: Semisubgroup coordinates for “ o$o − Ž 2 “ = 0, J. Math. Phys., Vol. 16, pp. 2507–2516, 1975. Kalnins, E. and Miller, W. (Jr.), Lie theory and separation of variables, 9: Orthogonal ” -separable coordinate systems for the wave equation “ •$• − Ž 2 “ = 0, J. Math. Phys., Vol. 17, pp. 331–335, 1976. Kalnins, E. and Miller, W. (Jr.), Lie theory and separation of variables, 10: Nonorthogonal ” separable solutions of the wave equation “ •$• − Ž 2 “ = 0, J. Math. Phys., Vol. 17, pp. 356–368, 1976. Kamke, E., Differentialgleichungen: Lo¨ sungsmethoden und Lo¨ sungen, I, Gew¨ohnliche Differentialgleichungen, B. G. Teubner, Leipzig, 1977. Kamke, E., Differentialgleichungen: Lo¨ sungsmethoden und Lo¨ sungen, II, Partielle Differentialgleichungen Erster Ordnung fu¨ r eine gesuchte Funktion, Akad. Verlagsgesellschaft Geest & Portig, Leipzig, 1965. Kanwal, R. P., Generalized Functions. Theory and Technique, Academic Press, Orlando, 1983. Korn, G. A. and Korn, T. M., Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York, 1968. Koshlyakov, N. S., Gliner, E. B., and Smirnov, M. M., Partial Differential Equations of Mathematical Physics [in Russian], Vysshaya Shkola, Moscow, 1970. Krein, S. G. (Editor), Functional Analysis [in Russian], Nauka, Moscow, 1972. Krylov, A. N., Collected Works: III Mathematics, Pt. 2 [in Russian], Izd-vo AN SSSR, Moscow, 1949. Lamb, H., Hydrodynamics, Dover Publ., New York, 1945. Lavrent’ev, M. A. and Shabat B. V., Methods of Complex Variable Theory [in Russian], Nauka, Moscow, 1973. Lavrik, V. I. and Savenkov, V. N., Handbook of Conformal Mappings [in Russian], Naukova Dumka, Kiev, 1970. Landau, L. D. and Lifshits, E. M., Quantum Mechanics. Nonrelativistic Theory [in Russian], Nauka, Moscow, 1974. Lebedev, N. N., Skal’skaya, I. P., and Uflyand, Ya. S., Collection of Problems on Mathematical Physics [in Russian], Gostekhizdat, Moscow, 1955. Leis, R., Initial-Boundary Value Problems in Mathematical Physics, John Wiley & Sons, Chichester, 1986. Levich, V. G., Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, New Jersey, 1962. Levitan, B. M. and Sargsyan, I. S., Sturm–Liouville and Dirac Operators [in Russian], Nauka, Moscow, 1988. Loitsyanskiy, L. G., Mechanics of Liquids and Gases, Begell House, New York, 1996. Lykov, A. V., Theory of Heat Conduction [in Russian], Vysshaya Shkola, Moscow, 1967. Mackie, A. G., Boundary Value Problems, Scottish Academic Press, Edinburgh, 1989. Makarov, A., Smorodinsky, J., Valiev, K., and Winternitz, P., A systematic search for nonrelativistic systems with dynamical symmetries. Part I: The integrals of motion, Nuovo Cimento, Vol. 52A, pp. 1061–1084, 1967. Marchenko, V. A., Sturm–Liouville Operators and Applications, Birkhauser Verlag, Basel-Boston, 1986. Markeev, A. P., Theoretical Mechanics [in Russian], Nauka, Moscow, 1990. Mathematical Encyclopedia [in Russian], Sovetskaya Entsiklopediya, Moscow, 1977. McLachlan, N. W., Theory and Application of Mathieu Functions, Clarendon Press, Oxford, 1947.

© 2002 by Chapman & Hall/CRC Page 772

REFERENCES

773

Meixner, J. and Sch¨afke, F., Mathieusche Funktionen und Spha¨ roidfunktionnen, Springer-Verlag, Berlin, 1965. Mikhlin, S. G., Variational Methods in Mathematical Physics [in Russian], Nauka, Moscow, 1970. Miles, J. W., Integral Transforms in Applied Mathematics, Cambridge Univ. Press, Cambridge, 1971. Miller, W. (Jr.), Symmetry and Separation of Variables, Addison-Wesley, London, 1977. Miller, J. (Jr.) and Rubel, L. A., Functional separation of variables for Laplace equations in two dimensions, J. Phys. A, Vol. 26, No. 8, pp. 1901–1913, 1993. Moon, P. and Spencer, D., Field Theory Handbook, Springer-Verlag, Berlin, 1961. Morse, P. M. and Feshbach, H., Methods of Theoretical Physics, Vols. 1–2, McGraw-Hill, New York, 1953. Murphy, G.M., Ordinary Differential Equations and Their Solutions, D. Van Nostrand, New York, 1960. Myint-U, T. and Debnath, L., Partial differential equations for scientists and engineers, NorthHolland Publ., New York, 1987. Naimark, M. A., Linear Differential Operators [in Russian], Nauka, Moscow, 1969. Niederer, U., The maximal kinematical invariance group of the harmonic oscillator, Helv. Phys. Acta, Vol. 46, pp. 191–200, 1973. Nikiforov, A. F. and Uvarov, V. B., Special Functions of Mathematical Physics. A Unified Introduction with Applications, Birkhauser Verlag, Basel-Boston, 1988. Novikov, E. A., Concerning turbulent diffusion in a stream with a transverse gradient of velosity, Appl. Math. Mech. (PMM), Vol. 22, No. 3, p. 412–414, 1958. Nusselt, W., Abh¨angigkeit der W¨arme¨ubergangzahl con der Rohra¨ nge, VDI Zeitschrift, Bd. 54, No. 28, S. 1154–1158, 1910. Olver, P. J., Application of Lie Groups to Differential Equations, Springer-Verlag, New York, 1986. Ovsiannikov, L. V., Group Analysis of Differential Equations, Academic Press, New York, 1982. Pavlovskii, Yu. N., Analysis of some invariant solutions of boundary layer equations, Zh. Bych. Matem. i Mat. Fiziki, Vol. 1, No. 2, pp. 280–294, 1961. Petrovsky, I. G., Lectures on Partial Differential Equations, Dover Publ., New York, 1991. Pinsky, M. A., Introduction to Partial Differential Equations with Applications, McGraw-Hill, New York, 1984. Polozhii, G. N., Mathematical Physics Equations [in Russian], Vysshaya Shkola, Moscow, 1964. Polyanin, A. D., The structure of solutions of linear nonstationary boundary-value problems of mechanics and mathematical physics, Doklady Physics, Vol. 45, No. 8, pp. 415–418, 2000a. Polyanin, A. D., Partial separation of variables in unsteady problems of mechanics and mathematical physics, Doklady Physics, Vol. 45, No. 12, pp. 680–684, 2000b. Polyanin, A. D., Linear problems of heat and mass transfer: general relations and results, Theor. Found. Chem. Eng., Vol. 34, No. 6, pp. 509–520, 2000c. Polyanin, A. D., Handbook of Linear Mathematical Physics Equations [in Russian], Fizmatlit, Moscow, 2001a. Polyanin, A. D., Transformations and exact solutions of boundary layer equations with arbitrary functions, Doklady AN, Vol. 379, No. 3, 2001b. Polyanin, A. D., Exact solutions and transformations of the equations of a stationary laminar boundary layer, Theor. Found. Chem. Eng., Vol. 35, No. 4, pp. 319–328, 2001c. Polyanin, A. D., Generalized separable solutions of Navier–Stokes equations, Doklady AN, Vol. 380, No. 4, 2001d.

© 2002 by Chapman & Hall/CRC Page 773

774

REFERENCES

Polyanin, A. D. and Dilman, V. V., Methods of Modeling Equations and Analogies in Chemical Engineering, CRC Press, Boca Raton, 1994. Polyanin, A. D., Kutepov, A. M., Vyazmin, A. V., and Kazenin, D. A., Hydrodynamics, Mass and Heat Transfer in Chemical Engineering, Gordon & Breach Sci. Publ., London, 2001. Polyanin, A. D. and Manzhirov, A. V., Handbook of Integral Equations, CRC Press, Boca Raton, 1998. Polyanin, A. D., Vyazmin, A. V., Zhurov, A. I., and Kazenin, D. A., Handbook of Exact Solutions of Heat and Mass Transfer Equations [in Russian], Faktorial, Moscow, 1998. Polyanin, A. D. and Zaitsev, V. F., Handbook of Exact Solutions for Ordinary Differential Equations, CRC Press, Boca Raton, 1995. Polyanin, A. D., Zaitsev, V. F., and Moussiaux, A., Handbook of First Order Partial Differential Equations, Gordon & Breach, London, 2001. Polyanin, A. D. and Zhurov, A. I., Exact solutions to nonlinear equations of mechanics and mathematical physics, Doklady Physics, Vol. 43, No. 6, pp. 381–385, 1998. Polyanin, A. D., Zhurov, A. I., and Vyazmin, A. V., Generalized separation of variables in nonlinear heat and mass transfer equations, J. Non-Equilibrium Thermodynamics, Vol. 25, No. 3/4, pp. 251–267, 2000. Prudnikov, A. P., Brychkov, Yu. A., and Marichev, O. I., Integrals and Series, Vol. 1, Elementary Functions, Gordon & Breach Sci. Publ., New York, 1986. Prudnikov, A. P., Brychkov, Yu. A., and Marichev, O. I., Integrals and Series, Vol. 2, Special Functions, Gordon & Breach Sci. Publ., New York, 1986. Pukhnachev, V. V., Group properties of the Navier–Stokes equations in the plane case, Zh. Prikl. Mekh. i Tekhn. Fiziki, No. 1, pp. 83–90, 1960. Rimmer, P. L., Heat transfer from a sphere in a stream of small Reynolds number, J. Fluid Mech., Vol. 32, No. 1, pp. 1–7, 1968. Rotem, Z., and Neilson, J. E., Exact solution for diffusion to flow down an incline, Can. J. Chem. Engng., Vol. 47, pp. 341–346, 1966. Schlichting, H., Boundary Layer Theory, McGraw-Hill, New York, 1981. Sedov, L. I., Plane Problems of Hydrodynamics and Airdynamics [in Russian], Nauka, Moscow, 1980. Shilov, G. E., Mathematical Analysis: A Second Special Course [in Russian], Nauka, Moscow, 1965. Smirnov, V. I., A Course of Higher Mathematics. Vols. 2–3 [in Russian], Nauka, Moscow, 1974. Smirnov, M. M., Second Order Partial Differential Equations [in Russian], Nauka, Moscow, 1964. Smirnov, M. M., Problems on Mathematical Physics Equations [in Russian], Nauka, Moscow, 1975. Sneddon, I., Fourier Transformations, McGraw-Hill, New York, 1951. Stakgold, I., Boundary Value Problems of Mathematical Physics. Vols. I, II, SIAM, Philadelphia, 2000. Strauss, W. A., Partial Differential Equations. An Introduction, John Wiley & Sons, New York, 1992. Sutton, W. G. L., On the equation of diffusion in a turbulent medium, Proc. Poy. Soc., Ser. A, Vol. 138, No. 988, pp. 48–75, 1943. Svirshchevskii, S. R., Lie–Ba¨ cklund symmetries of linear ODEs and generalized separation of variables in nonlinear equations, Phys. Letters A, Vol. 199, pp. 344–348, 1995. Taylor, M., Partial Differential Equations, Vol. 3, Springer-Verlag, New York, 1996. Temme, N. M., Special Functions. An Introduction to the Classical Functions of Mathematical Physics, Wiley-Interscience Publ., New York, 1996.

© 2002 by Chapman & Hall/CRC Page 774

REFERENCES

775

Tikhonov, A. N. and Samarskii, A. A., Equations of Mathematical Physics, Dover Publ., New York, 1990. Thomas, H. C., Heterogeneous ion exchange in a flowing system, J. Amer. Chem. Soc., Vol. 66, pp. 1664–1666, 1944. Tomotika, S. and Tamada, K., Studies on two-dimensional transonic flows of compressible fluid, Part 1, Quart. Appl. Math., Vol. 7, p. 381, 1950. Urvin, K. and Arscott, F., Theory of the Whittaker–Hill equation, Proc. Roy. Soc., Vol. A69, pp. 28–44, 1970. Vereshchagina, L. I., Group fibering of the spatial nonstationary boundary layer equations, Vestnik LGU, Vol. 13, No. 3, pp. 82–86, 1973. Vladimirov, V. S., Mikhailov, V. P., Vasharin A. A., et al., Collection of Problems on Mathematical Physics Equations [in Russian], Nauka, Moscow, 1974. Vladimirov, V. S., Mathematical Physics Equations [in Russian], Nauka, Moscow, 1988. Vvedensky, D., Partial Differential Equations, Addison-Wesley, Wakingham, 1993. Whittaker, E. T. and Watson, G. N., A Course of Modern Analysis, Vols. 1–2, Cambridge Univ. Press, Cambridge, 1952. Zachmanoglou, E. C. and Thoe, D. W., Introduction to Partial Differential Equations with Applications, Dover Publ., New York, 1986. Zaitsev, V. F. and Polyanin, A. D., Handbook of Partial Differential Equations: Exact Solutions [in Russian], MP Obrazovaniya, Moscow, 1996. Zauderer, E., Partial Differential Equations of Applied Mathematics, Wiley–Interscience Publ., New York, 1989. Zhdanov, R. Z., Separation of variables in the non-linear wave equation, J. Phys. A, Vol. 27, pp. L291–L297, 1994. Zwillinger, D., Handbook of Differential Equations, Academic Press, San Diego, 1998.

© 2002 by Chapman & Hall/CRC Page 775