메뉴 건너뛰기




Volumn 15, Issue 2, 1998, Pages 115-136

Lie-Bäcklund and Noether Symmetries with Applications

Author keywords

Conservation laws; Euler Lagrange; Lagrangians; Lie B cklund; Noether; Symmetries

Indexed keywords

EQUATIONS OF MOTION; LAGRANGE MULTIPLIERS; PARTIAL DIFFERENTIAL EQUATIONS; VARIATIONAL TECHNIQUES;

EID: 0032001026     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008240112483     Document Type: Article
Times cited : (127)

References (24)
  • 1
    • 0039826170 scopus 로고
    • Sur l'équivalence des équations d'evolution qui admettent une algèbre de Lie-Bäcklund infinie
    • Ibragimov, N. H., 'Sur l'équivalence des équations d'evolution qui admettent une algèbre de Lie-Bäcklund infinie', C.R. Academy of Sciences, Paris, ser. 1 293(14), 1981, 657-660.
    • (1981) C.R. Academy of Sciences, Paris, Ser. 1 , vol.293 , Issue.14 , pp. 657-660
    • Ibragimov, N.H.1
  • 3
    • 0003943074 scopus 로고
    • A History of the Calculus of Variations from the 17th through the 19th Century
    • Springer-Verlag, New York
    • Goldstine, H. H., A History of the Calculus of Variations from the 17th through the 19th Century, Studies in the History of Mathematical and Physical Sciences, Vol. 5, Springer-Verlag, New York, 1980.
    • (1980) Studies in the History of Mathematical and Physical Sciences , vol.5
    • Goldstine, H.H.1
  • 4
    • 2342601230 scopus 로고
    • On the theory of Lie-Bäcklund transformation groups
    • Ibragimov, N. H., 'On the theory of Lie-Bäcklund transformation groups', Matematicheskii Sbornik 102(2), 1979, 229-253. (English translation in Mathematics of the USSR-Sbornik 37(2), 1980, 205-226.)
    • (1979) Matematicheskii Sbornik , vol.102 , Issue.2 , pp. 229-253
    • Ibragimov, N.H.1
  • 5
    • 84916752451 scopus 로고
    • English translation
    • Ibragimov, N. H., 'On the theory of Lie-Bäcklund transformation groups', Matematicheskii Sbornik 102(2), 1979, 229-253. (English translation in Mathematics of the USSR-Sbornik 37(2), 1980, 205-226.)
    • (1980) Mathematics of the USSR-Sbornik , vol.37 , Issue.2 , pp. 205-226
  • 8
    • 84856365344 scopus 로고
    • The Noether identity
    • Institute of Hydrodynamics, USSR Ac. Sc., Novorsibirsk
    • Ibragimov, N. H., 'The Noether identity', in Continuum Dynamics, Institute of Hydrodynamics, USSR Ac. Sc., Novorsibirsk, 1979, Vol. 28, pp. 26-32.
    • (1979) Continuum Dynamics , vol.28 , pp. 26-32
    • Ibragimov, N.H.1
  • 10
    • 84930761411 scopus 로고
    • English translation
    • Noether, E., 'Invariante Variationsprobleme', Nachrichten der Akademie der Wissenschaften in Göttingen, Mathematisch-Physikalische Klasse 2, 1918, 235-257. (English translation in Transport Theory and Statistical Physics 1(3), 1971, 186-207.)
    • (1971) Transport Theory and Statistical Physics , vol.1 , Issue.3 , pp. 186-207
  • 14
    • 0342986633 scopus 로고    scopus 로고
    • Bertrand's theorem and its generalisation in classical mechanics
    • N. H. Ibragimov, F. M. Mahomed, D. P. Mason, and D. Sherwell (eds.), New Age International Publishers, New Delhi
    • Mahomed, F. M. and Vawda, F., 'Bertrand's theorem and its generalisation in classical mechanics', in Differential Equations and Chaos: Lectures on Selected Topics, N. H. Ibragimov, F. M. Mahomed, D. P. Mason, and D. Sherwell (eds.), New Age International Publishers, New Delhi, 1996, pp. 267-303.
    • (1996) Differential Equations and Chaos: Lectures on Selected Topics , pp. 267-303
    • Mahomed, F.M.1    Vawda, F.2
  • 15
    • 0001003724 scopus 로고
    • Generalization of Noether's theorem in classical mechanics
    • Sarlet, W. and Cantrijn, F., 'Generalization of Noether's theorem in classical mechanics', SIAM Review 23, 1981, 467-494.
    • (1981) SIAM Review , vol.23 , pp. 467-494
    • Sarlet, W.1    Cantrijn, F.2
  • 16
    • 2342490583 scopus 로고
    • Reduction of differential equations using Lie and Noether symmetries
    • Proceedings of the International Conference on Modern Group Analysis V, Johannesburg, South Africa, January 16-22, 1994, N. H. Ibragimov and F. M. Mahomed (eds.)
    • Kara, A. H., Mahomed, F. M., and Adam, A. A., 'Reduction of differential equations using Lie and Noether symmetries', Proceedings of the International Conference on Modern Group Analysis V, Johannesburg, South Africa, January 16-22, 1994, N. H. Ibragimov and F. M. Mahomed (eds.), Lie Groups and Their Applications 1(1), 1994, pp. 137-145.
    • (1994) Lie Groups and Their Applications , vol.1 , Issue.1 , pp. 137-145
    • Kara, A.H.1    Mahomed, F.M.2    Adam, A.A.3
  • 17
    • 0003111289 scopus 로고
    • Symmetries of first integrals and solutions of differential equations
    • Kara, A. H., Vawda, F. E., and Mahomed, F. M., 'Symmetries of first integrals and solutions of differential equations', Lie Groups and Their Applications 1(2), 1994, 27-48.
    • (1994) Lie Groups and Their Applications , vol.1 , Issue.2 , pp. 27-48
    • Kara, A.H.1    Vawda, F.E.2    Mahomed, F.M.3
  • 19
    • 0003143579 scopus 로고
    • Variational principles for second-order quasi-linear scalar equations
    • Anderson, I. M. and Duchamp, T. E., 'Variational principles for second-order quasi-linear scalar equations', Journal of Differential Equations 51, 1984, 1-47.
    • (1984) Journal of Differential Equations , vol.51 , pp. 1-47
    • Anderson, I.M.1    Duchamp, T.E.2
  • 20
    • 0039860402 scopus 로고
    • Symmetry vector fields and similarity solutions of nonlinear field equation describing the relaxation to a Maxwell distribution
    • Euler, N., Leach, P. G. L., Mahomed, F. M., and Steeb, W.-H., 'Symmetry vector fields and similarity solutions of nonlinear field equation describing the relaxation to a Maxwell distribution', International Journal of Theoretical Physics 27, 1988, 717-723.
    • (1988) International Journal of Theoretical Physics , vol.27 , pp. 717-723
    • Euler, N.1    Leach, P.G.L.2    Mahomed, F.M.3    Steeb, W.-H.4
  • 21
    • 2342654854 scopus 로고
    • Evolution equations II: General case
    • N. H. Ibragimov (ed.), CRC Press, Boca Raton, FL
    • Gazizov, R. K., 'Evolution equations II: General case', in CRC Handbook of Lie Group Analysis of Differential Equations, N. H. Ibragimov (ed.), CRC Press, Boca Raton, FL, 1994, Vol. 1, p. 194.
    • (1994) CRC Handbook of Lie Group Analysis of Differential Equations , vol.1 , pp. 194
    • Gazizov, R.K.1
  • 22
    • 2342601057 scopus 로고
    • Second-order partial differential equations with two independent variables
    • N. H. Ibragimov (ed.), CRC Press, Boca Raton, FL
    • Gazizov, R. K. and Ibragimov, N. H., 'Second-order partial differential equations with two independent variables', in CRC Handbook of Lie Group Analysis of Differential Equations, N. H. Ibragimov (ed.), CRC Press, Boca Raton, FL, 1994, Vol. 1, pp. 86-101.
    • (1994) CRC Handbook of Lie Group Analysis of Differential Equations , vol.1 , pp. 86-101
    • Gazizov, R.K.1    Ibragimov, N.H.2
  • 23
    • 0039324396 scopus 로고
    • Nonisentropic one-dimensional gas motions constructed by means of the contact group of the nonhomogeneous Monge-Ampère equation
    • Khabirov, S. V., 'Nonisentropic one-dimensional gas motions constructed by means of the contact group of the nonhomogeneous Monge-Ampère equation', Matematicheskii Sbornik 181(12), 1990, 1607-1615. (English translation in Mathematics of the USSR-Sbornik 71(2), 1992, 447-454.)
    • (1990) Matematicheskii Sbornik , vol.181 , Issue.12 , pp. 1607-1615
    • Khabirov, S.V.1
  • 24
    • 33947152644 scopus 로고
    • English translation
    • Khabirov, S. V., 'Nonisentropic one-dimensional gas motions constructed by means of the contact group of the nonhomogeneous Monge-Ampère equation', Matematicheskii Sbornik 181(12), 1990, 1607-1615. (English translation in Mathematics of the USSR-Sbornik 71(2), 1992, 447-454.)
    • (1992) Mathematics of the USSR-Sbornik , vol.71 , Issue.2 , pp. 447-454


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.