|
REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
| |
1
|
ANI)ERS(.)N, R.. L.. AND IBRAGIMOV: _~. K. Lie- Bdcklund Tt'ansformations in Applications. SIAM, Ptfiladclphia, 1979.
|
| |
2
|
AUTONNE. L. Sur la limitation du (legr~ pour les intdgrales algcbriques de l'dxluation diff~rent.ielle du premier ordrc. Journal de l'E, cole Polytechnique cah. 63, p. 79.-183; cah. 64. p. 1-53 (11893).
|
| |
3
|
BEKE. E. Die Irre(luciMlit~it der homogene linearen Differentialgleichungen. Math. Annale.n 45 (1894), 278- 300.
|
 |
4
|
|
 |
5
|
F. Boulier , D. Lazard , F. Ollivier , M. Petitot, Representation for the radical of a finitely generated differential ideal, Proceedings of the 1995 international symposium on Symbolic and algebraic computation, p.158-166, July 10-12, 1995, Montreal, Quebec, Canada
[doi> 10.1145/220346.220367]
|
 |
6
|
|
| |
7
|
Dhnl4oux, G. M~moire sur les dquations diffdrenr.ielh;s algS.briques du premier ordre et du premier dcgr6. Bull. des Science.s Math. et Astron. 2 (1878), 60 96, 123--144, 151--200.
|
| |
8
|
|
| |
9
|
HARAOKA, Y. The Galois theory for linear homogeneous partial differential equations of the first order. Funkciala~ Ekvacioj 3,? (199(1), 79 126.
|
| |
10
|
,JANET, h/{. Legons sur les systi:mes d'equations au, x derivdes particlles. Gmlticr-Villard, 1929.
|
| |
11
|
KAPTS()V: O. V. Classification of evolution e(tuations by conservation laws. Func.tional Anat. and its Appl. 16, 1 (1982), 59-61.
|
| |
12
|
KC)NIGSBE.R.(IER. L. Allgemeine Unter.s'uchungen aus der Theorie dcr Differentialgle.ichur~,gen. Leipzig, T(-'ubher, 1882.
|
| |
13
|
|
| |
14
|
|
| |
15
|
LE R()ux, J. Sur l'int.e'gration des dquat;ions diffe'.rentielles. Comptes Rend. Acad. Sci. Paris 143 (1906), 820-822.
|
| |
16
|
LOEWY, A. 0ber reduzible lineare homogene Differentialgleichungen. Math. Annalen 56 (1903). 549-584.
|
| |
17
|
LOEWY, A. Llber vollstandig reduzibh.', lineare homogene Difi'crentialgleiclnmgen. Math. Annalen 62 (1906), 89. 117.
|
| |
18
|
M:ANSFII-'I,{). E. Differential Groebner Bases. Ph.D. thesis., Universit.y of Sydney, Sydney, 1991.
|
| |
19
|
()l~El.\'IKOV, V. A. On tr,~nscend('ncy and algebraic indet)endencc of va.lues of' some entire flmctions. Soviet Math. - Izvestia. 1 (1968).
|
| |
20
|
OLVER: P. Applications of Lie groups to differential equations. Si)ringer-\::erlag, I986.
|
| |
21
|
PAINI,E.VE, P. M~moire sur los ~quations diffdrentielles du premier ordre. Annales Ecole Norm. Supdr. 8--9 (1891 1892), 9-58, 103-140. 201-226, 276-284; v. 9: l). 9-3{). 101-144, 283-308. sec also Oeuvres, v. 2, I7. 237-461.
|
| |
22
|
POMMAI~ET, J. F. Systems of partial differential equations and Lie pseudogroups. Gor(lon & Breach, 1978.
|
| |
23
|
REID, G..l. Algorithms for reducing a system of pdes to standard form, detcrlnining the dimension of its s()- lution space and cah:ulating its taylor series solutimls. Euro. J. Appl. Mec.h. 2 (1991), 293-318.
|
| |
24
|
RIQUIER, C. Le.~ system~:s d'equations aux dcrivde, s partielles. Gmltier-\rillard. 1910.
|
| |
25
|
|
| |
26
|
Sa{.fK~t()'v', V. K. On differentia/ irreducibility of a class of differ(rntial equations. Soviet Math.. - lzvestia, 1 (1980).
|
| |
27
|
SCHWARZ. F. The R.iquier-Jartet. theory and its a.pplica.tions to nonlinear evolution equations. Physica D 11 (1984). 2.13 351.
|
| |
28
|
S1x(:;En, M. F. Liouvillian first int, egrals of differentia.1 equat.ions. Trans. AMS 333 (1.992). 673-688.
|
| |
29
|
SOSNIN, M. Decon~position of polynomial ordinary diffb.xential cq~mtions. Krasnoyarsk, to be published, 1999.
|
| |
30
|
TH(:)MAS, J. M. Differe.ntial ,systems. AMS Coll. Publications, v. 21. 1937.
|
| |
31
|
TSAREV. S. P. On some prol)lenls in factorization of lin(.'.ar ordinary diff(,rential operators. Programming 6~ computer software 20, 1 (1994), 27--29.
|
 |
32
|
|
 |
33
|
|
| |
34
|
TSAREV, S. P. Fa(:torization of linear pm'- tial differential operators and Darboux integrability of nonlinem' PDEs. ISSAC'98 Poster, 1998. obtaina.ble froln (:s(~.xxx.lanl.gov: Computer Science e-print cs/9811002, INTERNET UR.L: l,ttp://xxx.lanl, gov/abs/cs. SC/9811002.
|
| |
35
|
U.~tEM(JI~A, H. Oll the irreducibility of the first differential equation of Painlevd. In Alge.braic g(~ometry and commutative algebra, in honor of Masayoshi Nagata, Tokyo. 1987, pp. 101-119.
|
| |
36
|
UME.X~URA, H. Differential Galois theory of infinite dimension. Na.qoya Math. Journal I4~ (1996), 59--135.
|
| |
37
|
UMF.MUi~A, H. Galois theory of algebraic and differential equations. Nagoya Math. Journal 144 (1996), 1-58.
|
| |
38
|
|
| |
39
|
|
| |
40
|
WEIL, J.-A. Constantes et polynSmes de Darboux en alg~'.bre dif.-.-J~rentielle: application aux syst~mes diffdrenticIs lindaires. Ph. D. diss., t~.(:ole Polytectlnique, Paris, 1995.
|
| |
41
|
ZIPPEL,, R. Rational function decomposition. Tech. Rep. TR 91-12{}9, Department of Computcr Science. Cornell University. 1991.
|
|