메뉴 건너뛰기




Volumn 1, Issue 4, 2001, Pages 335-383

Algorithms for Symmetric Differential Systems

Author keywords

[No Author keywords available]

Indexed keywords

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0042461645     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s002080010014     Document Type: Article
Times cited : (26)

References (42)
  • 1
    • 0002004721 scopus 로고
    • Solitons, Nonlinear Evolution Equations and Inverse Scattering
    • Cambridge University Press, Cambridge
    • M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, London Mathematical Society Lecture Notes in Mathematics, Vol. 149, Cambridge University Press, Cambridge, 1991.
    • (1991) London Mathematical Society Lecture Notes in Mathematics , vol.149
    • Ablowitz, M.J.1    Clarkson, P.A.2
  • 3
    • 0000133634 scopus 로고
    • Representation for the radical of a finitely generated differential ideal
    • (A. Levelt, ed.), ACM Press, New York
    • F. Boulier, D. Lazard, F. Ollivier, and M. Petitot, Representation for the radical of a finitely generated differential ideal, in Proc. ISSAC '95 (A. Levelt, ed.), ACM Press, New York, 1995.
    • (1995) Proc. ISSAC '95
    • Boulier, F.1    Lazard, D.2    Ollivier, F.3    Petitot, M.4
  • 4
    • 85034654309 scopus 로고
    • Applications of Gröbner bases in non-linear computational geometry
    • Mathematical Aspects of Scientific Software (J. R. Rice, ed.), Springer-Verlag, New York
    • B. Buchberger, Applications of Gröbner bases in non-linear computational geometry, in Mathematical Aspects of Scientific Software (J. R. Rice, ed.), IMA Volumes in Mathematics and its Applications, Vol. 14, Springer-Verlag, New York, 1988, pp. 52-80.
    • (1988) IMA Volumes in Mathematics and Its Applications , vol.14 , pp. 52-80
    • Buchberger, B.1
  • 5
    • 85034782464 scopus 로고
    • Groebner bases and differential algebra
    • Proceedings AAECC (L. Huguet and A. Poli, eds.), Springer-Verlag, Berlin
    • G. Carrà-Ferro, Groebner bases and differential algebra, in Proceedings AAECC (L. Huguet and A. Poli, eds.), Lecture Notes in Computer Science, Vol. 356. Springer-Verlag, Berlin, 1989, pp. 129-140.
    • (1989) Lecture Notes in Computer Science , vol.356 , pp. 129-140
    • Carrà-Ferro, G.1
  • 8
    • 84876653157 scopus 로고
    • private communication
    • C. M. Cosgrove, private communication, 1991.
    • (1991)
    • Cosgrove, C.M.1
  • 11
  • 12
  • 13
    • 0002725268 scopus 로고
    • Second-order differential invariants of the rotation group O(n) and of its extensions: E(n). P(1, n), G(1, n)
    • W. I. Fushchich and I. A. Yegorchenko, Second-order differential invariants of the rotation group O(n) and of its extensions: E(n). P(1, n), G(1, n), Acta Appl. Math. 28 (1992), 69-92.
    • (1992) Acta Appl. Math. , vol.28 , pp. 69-92
    • Fushchich, W.I.1    Yegorchenko, I.A.2
  • 14
    • 0002369953 scopus 로고
    • On the reduction of the nonlinear multidimensional wave equations and compatibility of the d'Alembert-Hamilton system
    • W. I. Fushchich, R. Z. Zhdanov and I. A. Yegorchenko, On the reduction of the nonlinear multidimensional wave equations and compatibility of the d'Alembert-Hamilton system, J. Math. Anal. Appl. 161 (1991), 352-360.
    • (1991) J. Math. Anal. Appl. , vol.161 , pp. 352-360
    • Fushchich, W.I.1    Zhdanov, R.Z.2    Yegorchenko, I.A.3
  • 15
    • 0348155700 scopus 로고    scopus 로고
    • Gröbner bases, invariant theory and equivariant dynamics
    • K. Gatermann and F. Guyard, Gröbner bases, invariant theory and equivariant dynamics, J. Symbolic Comput. 28 (1999), 275-302.
    • (1999) J. Symbolic Comput. , vol.28 , pp. 275-302
    • Gatermann, K.1    Guyard, F.2
  • 17
    • 85015125367 scopus 로고
    • A constructive implementation of the Cartan-Kahler theory of exterior differential systems
    • D. Hartley and R. W. Tucker, A constructive implementation of the Cartan-Kahler theory of exterior differential systems, J. Symbolic Comput. 12 (1991), 655-667
    • (1991) J. Symbolic Comput. , vol.12 , pp. 655-667
    • Hartley, D.1    Tucker, R.W.2
  • 18
    • 0030213443 scopus 로고    scopus 로고
    • LIE, a PC program for LIE analysis of differential equations
    • A. K. Head, LIE, a PC program for LIE analysis of differential equations, Comput. Phys. Comm. 96 (1996), 311-313.
    • (1996) Comput. Phys. Comm. , vol.96 , pp. 311-313
    • Head, A.K.1
  • 19
    • 0034178810 scopus 로고    scopus 로고
    • Factorisation free decomposition algorithms in differential algebra
    • E. Hubert, Factorisation free decomposition algorithms in differential algebra, J. Symbolic Comput. 29 (2000), 641-662.
    • (2000) J. Symbolic Comput. , vol.29 , pp. 641-662
    • Hubert, E.1
  • 22
    • 0031142055 scopus 로고    scopus 로고
    • Applications of the differential algebra package diffgrob2 to classical symmetries of differential equations
    • E. L. Mansfield and P. A. Clarkson, Applications of the differential algebra package diffgrob2 to classical symmetries of differential equations, J. Symbolic Comput. 23 (1997), 517-533.
    • (1997) J. Symbolic Comput. , vol.23 , pp. 517-533
    • Mansfield, E.L.1    Clarkson, P.A.2
  • 24
    • 0032477225 scopus 로고    scopus 로고
    • Nonclassical reductions of a 3 + 1 cubic nonlinear Schrödinger system
    • E. L. Mansfield, G. J. Reid and P. A. Clarkson, Nonclassical reductions of a 3 + 1 cubic nonlinear Schrödinger system, Comput. Phys. Comm. 115 (1998), 460-488.
    • (1998) Comput. Phys. Comm. , vol.115 , pp. 460-488
    • Mansfield, E.L.1    Reid, G.J.2    Clarkson, P.A.3
  • 26
    • 0002016585 scopus 로고    scopus 로고
    • The differential algebra package diffgrob2
    • E. L. Mansfield, The differential algebra package diffgrob2, MapleTech 3 (1996), 33-37.
    • (1996) MapleTech , vol.3 , pp. 33-37
    • Mansfield, E.L.1
  • 27
    • 84876650860 scopus 로고    scopus 로고
    • Computer algebra for the classification problem
    • (N. H. Ibragimov, K. R. Naqvi and E. Straume, eds.), Mars, Trondheim
    • E. L. Mansfield, Computer algebra for the classification problem, in Modern Group Analysis VII (N. H. Ibragimov, K. R. Naqvi and E. Straume, eds.), Mars, Trondheim, 1999, pp. 211-217.
    • (1999) Modern Group Analysis VII , pp. 211-217
    • Mansfield, E.L.1
  • 28
    • 0003419177 scopus 로고    scopus 로고
    • Springer-Verlag, New York, MAPLE and MAPLE V are registered trademarks of Waterloo Maple Inc.
    • M. B. Monagan et al., Maple Programming Guide, Springer-Verlag, New York, 1996. MAPLE and MAPLE V are registered trademarks of Waterloo Maple Inc.
    • (1996) Maple Programming Guide
    • Monagan, M.B.1
  • 29
    • 0003284228 scopus 로고    scopus 로고
    • Classical Invariant Theory
    • Cambridge University Press, Cambridge
    • P. J. Olver, Classical Invariant Theory, London Mathematical Society Student Texts, Vol. 44, Cambridge University Press, Cambridge, 1999.
    • (1999) London Mathematical Society Student Texts , vol.44
    • Olver, P.J.1
  • 32
    • 84876616344 scopus 로고    scopus 로고
    • private communication
    • P. J. Olver, private communication, 1998.
    • (1998)
    • Olver, P.J.1
  • 34
    • 84972029082 scopus 로고
    • Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution
    • G. J. Reid, Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution, European J. Appl. Math. 2 (1991), 293-318.
    • (1991) European J. Appl. Math. , vol.2 , pp. 293-318
    • Reid, G.J.1
  • 35
    • 0030364642 scopus 로고    scopus 로고
    • Reduction of systems of nonlinear partial differential equations to simplified involutive forms
    • G. J. Reid, A. D. Wittkopf and A. Boulton, Reduction of systems of nonlinear partial differential equations to simplified involutive forms, European J. Appl. Math. 7 (1996), 604-635.
    • (1996) European J. Appl. Math. , vol.7 , pp. 604-635
    • Reid, G.J.1    Wittkopf, A.D.2    Boulton, A.3
  • 37
    • 0030717962 scopus 로고    scopus 로고
    • Rankings of partial derivatives
    • (W. Küchlin, ed.), ACM Press, New York
    • C. J. Rust and G. J. Reid, Rankings of partial derivatives, in Proc. ISSAC '97 (W. Küchlin, ed.), ACM Press, New York, 1997, pp. 9-16.
    • (1997) Proc. ISSAC '97 , pp. 9-16
    • Rust, C.J.1    Reid, G.J.2
  • 40
    • 34250603285 scopus 로고
    • Sur les invariants différentiels des groupes continue de transformation
    • A. M. Tresse, Sur les invariants différentiels des groupes continue de transformation, Acta Math. 18 (1894), 1-88. (1992) 61-86.
    • (1894) Acta Math. , vol.18 , pp. 1-88
    • Tresse, A.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.