메뉴 건너뛰기




Volumn 25, Issue 3-5, 1996, Pages 303-322

How to build up variable transformations allowing one to map nonlinear hyperbolic equations into autonomous or linear ones

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0030503862     PISSN: 00411450     EISSN: None     Source Type: Journal    
DOI: 10.1080/00411459608220703     Document Type: Article
Times cited : (36)

References (33)
  • 1
    • 0023859612 scopus 로고
    • On the evolution of weak discontinuities in a state characterized by invariant solutions
    • W. F. Ames, A. Donato. On the evolution of weak discontinuities in a state characterized by invariant solutions. Int. J. Non-linear Mech., 23, 167-174, 1988.
    • (1988) Int. J. Non-linear Mech. , vol.23 , pp. 167-174
    • Ames, W.F.1    Donato, A.2
  • 2
    • 0343121387 scopus 로고
    • Group analysis approach in magnetohydrodynamics: Weak discontinuity propagation in a non-constant state
    • N. Manganaro, F. Oliveri. Group analysis approach in magnetohydrodynamics: weak discontinuity propagation in a non-constant state. Meccanica, 24, 71-78, 1989.
    • (1989) Meccanica , vol.24 , pp. 71-78
    • Manganaro, N.1    Oliveri, F.2
  • 3
    • 38248999266 scopus 로고
    • Reduction to autonomous form and exact solutions of axi-symmetric MHD equations
    • A. Donato, F. Oliveri. Reduction to autonomous form and exact solutions of axi-symmetric MHD equations. Math. Computer Modelling, 18, 83-90, 1993.
    • (1993) Math. Computer Modelling , vol.18 , pp. 83-90
    • Donato, A.1    Oliveri, F.2
  • 5
    • 0022075242 scopus 로고
    • Exact solutions for large amplitude waves in dispersive and dissipative systems
    • E. Varley, B. Seymour. Exact solutions for large amplitude waves in dispersive and dissipative systems. Stud. Appl. Math., 72, 241-262, 1985.
    • (1985) Stud. Appl. Math. , vol.72 , pp. 241-262
    • Varley, E.1    Seymour, B.2
  • 8
    • 0002950735 scopus 로고
    • A class of linearizable models and generation of material response functions to nonlinear hyperbolic heat conduction
    • D. Fusco, N. Manganaro, A class of linearizable models and generation of material response functions to nonlinear hyperbolic heat conduction. J. Math. Phys., 32, 3043-3046, 1991.
    • (1991) J. Math. Phys. , vol.32 , pp. 3043-3046
    • Fusco, D.1    Manganaro, N.2
  • 9
    • 0003362075 scopus 로고
    • Similarity Solutions of Non-Linear Partial Differential Equations
    • Pitman
    • L. Dresner. Similarity Solutions of Non-Linear Partial Differential Equations. Res. Notes in Math., 88, Pitman, 1983.
    • (1983) Res. Notes in Math. , vol.88
    • Dresner, L.1
  • 14
    • 0003157842 scopus 로고
    • When nonautonomous equations are equivalent to autonomous ones
    • A. Donato, F. Oliveri. When nonautonomous equations are equivalent to autonomous ones. Appl. Anal., 58, 313-323, 1995.
    • (1995) Appl. Anal. , vol.58 , pp. 313-323
    • Donato, A.1    Oliveri, F.2
  • 15
    • 0002944770 scopus 로고
    • Reduction to autonomous form by means of canonical variables
    • edited by S. Rionero & T. Ruggeri, World Scientific Publishing
    • A. Donato, F. Oliveri. Reduction to autonomous form by means of canonical variables. Proc. VII Int. Conf. on Waves and Stability in Continuous Media, edited by S. Rionero & T. Ruggeri, World Scientific Publishing, 23, 146-154, 1994.
    • (1994) Proc. VII Int. Conf. on Waves and Stability in Continuous Media , vol.23 , pp. 146-154
    • Donato, A.1    Oliveri, F.2
  • 16
    • 0000685028 scopus 로고
    • Linearization procedure of nonlinear first order systems of PDE's by means of canonical variables related to Lie groups of point transformations
    • A. Donato, F. Oliveri. Linearization procedure of nonlinear first order systems of PDE's by means of canonical variables related to Lie groups of point transformations. J. Math. Anal. Appl., 188, 552-568, 1994.
    • (1994) J. Math. Anal. Appl. , vol.188 , pp. 552-568
    • Donato, A.1    Oliveri, F.2
  • 17
    • 0002247504 scopus 로고
    • Review of symbolic software for the computation of Lie symmetries of differential equations
    • W. Hereman. Review of symbolic software for the computation of Lie symmetries of differential equations. Euromath Bulletin, 1, 45-82, 1994.
    • (1994) Euromath Bulletin , vol.1 , pp. 45-82
    • Hereman, W.1
  • 18
    • 0000914217 scopus 로고
    • Symbolic software for Lie symmetry analysis
    • To appear edited by N. H. Ibragimov, CRC Press, Boca Raton
    • W. Hereman. Symbolic software for Lie symmetry analysis. To appear in CRC Handbook of Lie group analysis of differential equations, vol. 3, edited by N. H. Ibragimov, CRC Press, Boca Raton, 1995.
    • (1995) CRC Handbook of Lie Group Analysis of Differential Equations , vol.3
    • Hereman, W.1
  • 19
    • 84980077727 scopus 로고
    • Hyperbolic systems of conservation laws II
    • P. D. Lax. Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math., 10, 537-566, 1957.
    • (1957) Comm. Pure Appl. Math. , vol.10 , pp. 537-566
    • Lax, P.D.1
  • 22
    • 0010899298 scopus 로고
    • Linearization of completely exceptional second order hyperbolic conservative equations
    • A. Donato, F. Oliveri. Linearization of completely exceptional second order hyperbolic conservative equations. Appl. Anal., 57, 35-45, 1995.
    • (1995) Appl. Anal. , vol.57 , pp. 35-45
    • Donato, A.1    Oliveri, F.2
  • 23
    • 0039038885 scopus 로고
    • The (3+1)-dimensional Monge-Ampère equation in discontinuity wave theory: Application of a reciprocal transformation
    • A. Donato, U. Ramgulam, C. Rogers. The (3+1)-dimensional Monge-Ampère equation in discontinuity wave theory: application of a reciprocal transformation. Meccanica, 27, 257-262, 1992.
    • (1992) Meccanica , vol.27 , pp. 257-262
    • Donato, A.1    Ramgulam, U.2    Rogers, C.3
  • 24
    • 0010826103 scopus 로고
    • Exceptionality condition and linearization procedure for a third order nonlinear PDE
    • A. Donato, G. Valenti. Exceptionality condition and linearization procedure for a third order nonlinear PDE. J. Math. Anal. Appl., 186, 375-382, 1994.
    • (1994) J. Math. Anal. Appl. , vol.186 , pp. 375-382
    • Donato, A.1    Valenti, G.2
  • 25
    • 0004483483 scopus 로고
    • Exact solutions of the equation describing cylindrical solitons
    • R. Hirota. Exact solutions of the equation describing cylindrical solitons. Phys. Lett., 71A, 393-394, 1979.
    • (1979) Phys. Lett. , vol.71 A , pp. 393-394
    • Hirota, R.1
  • 26
    • 0023559384 scopus 로고
    • On the similarity solutions of KdV equation with variable coefficients
    • F. Oliveri. On the similarity solutions of KdV equation with variable coefficients. Int. J. Non-linear Mech., 22, 467-475, 1987.
    • (1987) Int. J. Non-linear Mech. , vol.22 , pp. 467-475
    • Oliveri, F.1
  • 27
    • 7044278975 scopus 로고
    • Über das auffinden von Ähnlichkeitslösungen partieller differentialgleichungssysteme unter benutzung von transformationsgruppen, mit anwendungen auf probleme der strömungsphysik
    • E. A. Müller and K. Matschat, Über das auffinden von Ähnlichkeitslösungen partieller differentialgleichungssysteme unter benutzung von transformationsgruppen, mit anwendungen auf probleme der strömungsphysik. Miszellaneen der Angewandten Mechanik, 190-222, 1962.
    • (1962) Miszellaneen der Angewandten Mechanik , pp. 190-222
    • Müller, E.A.1    Matschat, K.2
  • 28
    • 7044256817 scopus 로고
    • Sulla integrazione di un sistema iperbolico quasi lineare di due equazioni in due variabili indipendenti completamente eccezionale
    • T. Ruggeri. Sulla integrazione di un sistema iperbolico quasi lineare di due equazioni in due variabili indipendenti completamente eccezionale. Riv. Mat. Univ. Parma, 4, 1-12, 1979.
    • (1979) Riv. Mat. Univ. Parma , vol.4 , pp. 1-12
    • Ruggeri, T.1
  • 29
    • 7044255363 scopus 로고
    • The occurrence of singularities in solutions of homogeneous systems of two first order quasilinear hyperbolic equations with smooth initial data
    • A. Jeffrey, A. Donato. The occurrence of singularities in solutions of homogeneous systems of two first order quasilinear hyperbolic equations with smooth initial data. Wave Motion, 1, 177-185, 1979.
    • (1979) Wave Motion , vol.1 , pp. 177-185
    • Jeffrey, A.1    Donato, A.2
  • 31
    • 0001118763 scopus 로고
    • Compressibility effects in aerodynamics
    • T. Von Kármán. Compressibility effects in aerodynamics. J. Aeron. Sc., 8, 337, 1941.
    • (1941) J. Aeron. Sc. , vol.8 , pp. 337
    • Von Kármán, T.1
  • 32
    • 7044277571 scopus 로고
    • On some first order systems reducible to Monge-Arnpère equations and their linearization
    • A. Donato, A. Palumbo. On some first order systems reducible to Monge-Arnpère equations and their linearization. Bull. Tech. Univ. Instanbul, 47, 101-113, 1994.
    • (1994) Bull. Tech. Univ. Instanbul , vol.47 , pp. 101-113
    • Donato, A.1    Palumbo, A.2
  • 33
    • 0001435725 scopus 로고
    • Sur l'équation générale de Monge-Ampère d'ordre supérieur
    • G. Boillat. Sur l'équation générale de Monge-Ampère d'ordre supérieur. C. R. Acad. Sci. Paris, Ser. I, 315, 1211-1214, 1992.
    • (1992) C. R. Acad. Sci. Paris, Ser. I , vol.315 , pp. 1211-1214
    • Boillat, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.