메뉴 건너뛰기




Volumn 42, Issue 8, 2001, Pages 3714-3734

An application of solvable structures to classical and nonclassical similarity solutions

(1)  Barco, M A a  

a NONE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035535333     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1368845     Document Type: Article
Times cited : (5)

References (31)
  • 1
    • 0000924529 scopus 로고
    • Über die integration durch bestimmte integrale von einer klasse linear partieller differentialgleichungen
    • S. Lie, "Über die Integration durch bestimmte Integrale von einer Klasse linear partieller Differentialgleichungen," Arch. Math. 6, 328-368 (1881).
    • (1881) Arch. Math. , vol.6 , pp. 328-368
    • Lie, S.1
  • 6
    • 0001193076 scopus 로고
    • Symmetry and explicit solutions of partial differential equations
    • P. J. Olver, "Symmetry and explicit solutions of partial differential equations," Appl. Numer. Math. 10, 307-324 (1992).
    • (1992) Appl. Numer. Math. , vol.10 , pp. 307-324
    • Olver, P.J.1
  • 10
    • 0007420103 scopus 로고
    • Some aspects of exterior differential systems
    • R A. Griffiths, "Some aspects of exterior differential systems," Proc. Symp. Pure Math. 53, 151-173 (1991).
    • (1991) Proc. Symp. Pure Math. , vol.53 , pp. 151-173
    • Griffiths, R.A.1
  • 11
    • 85015125367 scopus 로고
    • A constructive implementation of the Cartan Kahler theorem for exterior differential systems
    • D. Hartley and R. W. Tucker, "A constructive implementation of the Cartan Kahler theorem for exterior differential systems," J. Symbol. Comput. 12, 655-667 (1991).
    • (1991) J. Symbol. Comput. , vol.12 , pp. 655-667
    • Hartley, D.1    Tucker, R.W.2
  • 12
    • 0009069164 scopus 로고
    • Exterior differential systems and equivalence problems
    • Kluwer, Dordrecht
    • K. Yang, "Exterior differential systems and equivalence problems," Mathematics and its Applications (Kluwer, Dordrecht, 1992), Vol. 73.
    • (1992) Mathematics and Its Applications , vol.73
    • Yang, K.1
  • 13
    • 0040651088 scopus 로고
    • Geometric approach to invariance groups and solutions of partial differential systems
    • B. K. Harrison and F. B. Estabrook, "Geometric approach to invariance groups and solutions of partial differential systems." J. Math. Phys. 12, 653-666 (1971).
    • (1971) J. Math. Phys. , vol.12 , pp. 653-666
    • Harrison, B.K.1    Estabrook, F.B.2
  • 14
    • 0007450397 scopus 로고
    • On É. Cartan's prolongation theorem of exterior differential systems
    • M. Kuranishi, "On É. Cartan's prolongation theorem of exterior differential systems," Am. J. Math. 79, 1-47 (1957).
    • (1957) Am. J. Math. , vol.79 , pp. 1-47
    • Kuranishi, M.1
  • 18
    • 0003184354 scopus 로고    scopus 로고
    • Integrability by quadratures for systems ol involutive vector fields
    • 1991
    • P. Basarab-Horwath, "Integrability by quadratures for systems ol involutive vector fields," Ukr. Mat. Zh. 43, 1330-1337 (1991); English translation in Uk. Math. J. 43, 1236-1242 (1991).
    • Ukr. Mat. Zh. , vol.43 , pp. 1330-1337
    • Basarab-Horwath, P.1
  • 19
    • 0039789647 scopus 로고
    • English translation in
    • P. Basarab-Horwath, "Integrability by quadratures for systems ol involutive vector fields," Ukr. Mat. Zh. 43, 1330-1337 (1991); English translation in Uk. Math. J. 43, 1236-1242 (1991).
    • (1991) Uk. Math. J. , vol.43 , pp. 1236-1242
  • 20
    • 0001994828 scopus 로고
    • Symmetries of distributions and quadrature of ordinary differential equations
    • S. V. Duzhin and V. V. Lychagin, "Symmetries of distributions and quadrature of ordinary differential equations," Acta Appl. Math. 24, 29-57 (1991).
    • (1991) Acta Appl. Math. , vol.24 , pp. 29-57
    • Duzhin, S.V.1    Lychagin, V.V.2
  • 21
    • 21344491354 scopus 로고
    • Solvable structures and hidden symmetries
    • T. Hartl and C. Athorne, "Solvable structures and hidden symmetries," J. Phys. A 27, 3463-3471 (1994).
    • (1994) J. Phys. A , vol.27 , pp. 3463-3471
    • Hartl, T.1    Athorne, C.2
  • 22
    • 84968483729 scopus 로고
    • Geometric aspects of reduction of order
    • J. Sherring and G. E. Prince, "Geometric aspects of reduction of order," Trans. Am. Math. Soc. 334, 433-453 (1992).
    • (1992) Trans. Am. Math. Soc. , vol.334 , pp. 433-453
    • Sherring, J.1    Prince, G.E.2
  • 23
    • 0030586664 scopus 로고    scopus 로고
    • Non-classical solutions are non-existent for the heat equation and rare for non-linear diffusion
    • D. J. Arrigo, S. M. Goard, and P. Broadbridge, "Non-classical solutions are non-existent for the heat equation and rare for non-linear diffusion," J. Math. Anal. Appl. 202, 259-279 (1996).
    • (1996) J. Math. Anal. Appl. , vol.202 , pp. 259-279
    • Arrigo, D.J.1    Goard, S.M.2    Broadbridge, P.3
  • 24
    • 0000478462 scopus 로고
    • The general similarity solution of the heat equation
    • G. W. Bluman and J. D. Cole, "The general similarity solution of the heat equation," J. Math. Mech. 18, 1025-1042 (1969).
    • (1969) J. Math. Mech. , vol.18 , pp. 1025-1042
    • Bluman, G.W.1    Cole, J.D.2
  • 26
    • 0007376147 scopus 로고
    • Alternatives to the Cartan-Kähler theorem
    • D. G. B. Edelen, "Alternatives to the Cartan-Kähler theorem," Nonlin. Anal., Theory, Meth. Appl. 15, 765-786 (1990).
    • (1990) Nonlin. Anal., Theory, Meth. Appl. , vol.15 , pp. 765-786
    • Edelen, D.G.B.1
  • 28
    • 0007461217 scopus 로고
    • Symmetry transformations, isovectors, and conservation laws
    • G. Caviglia, "Symmetry transformations, isovectors, and conservation laws," J. Math. Phys. 27, 972-978 (1986).
    • (1986) J. Math. Phys. , vol.27 , pp. 972-978
    • Caviglia, G.1
  • 29
    • 84909574931 scopus 로고
    • Differential geometry as a tool for applied mathematicians
    • Geometrical Approaches to Differential Equations, Proceedings of the Fourth Scheveningen Conference, Scheveningen
    • F. B. Estabrook, "Differential geometry as a tool for applied mathematicians," Geometrical Approaches to Differential Equations, Proceedings of the Fourth Scheveningen Conference, Scheveningen, 1979 [Lect. Notes Math. 810, 1-22 1980].
    • (1979) Lect. Notes Math. , vol.810 , pp. 1-22
    • Estabrook, F.B.1
  • 30
    • 0007376580 scopus 로고    scopus 로고
    • Symmetry in differential form applications
    • to be published
    • M. A. Barco and G. E. Prince, "Symmetry in differential form applications," Acta. Appl. Math, (to be published).
    • Acta. Appl. Math
    • Barco, M.A.1    Prince, G.E.2
  • 31
    • 0031127274 scopus 로고    scopus 로고
    • DIMSYM and LIE: Symmetry determination packages
    • J. Sherring, A. K. Head, and G. E. Prince, "DIMSYM and LIE: Symmetry determination packages," Math. Comput. Modell. 25, 153-164 (1997).
    • (1997) Math. Comput. Modell. , vol.25 , pp. 153-164
    • Sherring, J.1    Head, A.K.2    Prince, G.E.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.