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Abstrakty
Making use of the ray theory and the method of asymptotic expansion of multiple scales, a study of the diffraction of weakly nonlinear waves in a direction transverse to the rays, through media described by dissipative or dispersive hyperbolic systems, is proposed. It is shown that the wave amplitude satisfies a generalized Zabolotskaya-Khokhlov equation in the dissipative case, or a generalized Kadomtsev-Petviashvili equation in the dispersive case. Moreover, plane, cylindrical and spherical waves are also investigated. The present approach is used to study wave diffraction in a heat-conducting fluid.
Słowa kluczowe
wave diffraction
transverse wave diffraction
wave propagation
wave equation
nonlinear differential equation
heat conduction
dispersive hyperbolic system
dissipative hyperbolic system
Zabolotskaya-Khokhlov equation
Kadomtsey-Petviashvili equation
spherical wave
cylindrical wave
weakly nonlinear waves
irreversible thermodynamics
Czasopismo
Rocznik
Tom
Strony
55--69
Opis fizyczny
Bibliogr. 17 poz.,
Twórcy
autor
- Department of Mathematics University of Messina Contrada Papardo, Salita Sperone, 31, 98166 Messina, Italy
autor
- Department of Mathematics University of Messina Contrada Papardo, Salita Sperone, 31, 98166 Messina, Italy
autor
- Department of Mathematics University of Messina Contrada Papardo, Salita Sperone, 31, 98166 Messina, Italy
Bibliografia
- 1. G. BOILLAT, La propagation des ondes, Gauthier-Villars, Paris 1965.
- 2. A. JEFFREY, Quasi-linear hyperbolic systems and waves, Pitman Publ., London 1976.
- 3. G.B. WHITAM, Linear and nonlinear waves, John Wiley &: Sons Inc., 1974.
- 4. G.A. NARIBOLI, The growth and propagation of waves in hypoelastic media, J. Math. Anal. Appl., 8, 57-65, 1964.
- 5. G.A. NARIBOLI, The propagation and. growth of sonic discontinuities in magnetohydrodynamics, J. Math, and Mech., 12, 141-148, 1963.
- 6. G.A. NARIBOLI, On some aspects of wave propagation, J Math, and Phys, Sci., 3, 294-309, 1968.
- 7. C. TRUESDELL, R.A. TOUPIN, Kinematics of singular surfaces. The classical field theories, Handb. Physik, 3/1, Ed. S. Flugge, Springer-Verlag, Berlin 1960.
- 8. D. Fusco, Some comments on wave motions described by nonhomogeneous quasi-linear first order hyperbolic systems, Meccanica, 17, 128-137, 1982.
- 9. D. Fusco, N. MANGANARO, Evolution equations compatible with quasilinear hyperbolic mod.els involving source-like terms, Research Report in Physics, Nonlinear Waves in Active Media, Ed. J. Engelgrecht, Springer-Verlag, Berlin, Heidelberg 17-23, 1989.
- 10. D. Fusco, A. PALUMBO, Dissipative or dispersive wave process ruled by first order quasi-linear systems involving source-like terms, Rend. Matematica, ser. VII, 9, 661-679, 1989.
- 11. F. CONFORTO, S. GIAMBO, Weakly non-linear high frequency waves for a first order quasi-linear systems involving source-like terms, Rend. Circ. Mat. Palermo, ser. II, XLIX, 205-220, 2000.
- 12. P. GERMAIN, Progressive waves, Jahrbuch der DGLR, 11-30, 1971.
- 13. S. GIAMB&, A. GRECO, P. PANTANO, Sur la rnethode perturbative et reductive a n-dimensions: le cas general, C.R. Acad. Sci. Paris, ser. A, 289, 553-557, 1979.
- 14. J.K. HUNTER, A ray method for slowly modulated waves, SIAM J. Appl. Math., 45, 5, 735-749, 1985.
- 15. J.K. HUNTER, Transverse diffraction of non-linear waves and singular rays, SIAM J. Appl. Math., 48, 1, 1-37, 1988.
- 16. D. Jou, J. CASAS-VAZQUEZ, G. LEBON, Extended irreversible thermodynamics, Rep. Prog. Phys., 51, 1105-1179, 1988.
- 17. M. TAJIRI, Similarity reductions of the Zabolotskaya-Khokhlov equation with a dissipative term, Nonlinear Mathematical Physics, 2, 3-4, 392-397, 1995.
Typ dokumentu
Bibliografia
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