A differential-difference bicomplex
Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 2, pp. 195-216 Cet article a éte moissonné depuis la source Math-Net.Ru

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We develop the method of difference jets on a multidimensional integer lattice. Based on this, we construct a lattice differential-difference bicomplex in the class of functions of a locally finite order and prove that it is acyclic.
Keywords: integer lattice, difference jet, differential-difference bicomplex.
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V. V. Zharinov. A differential-difference bicomplex. Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 2, pp. 195-216. http://geodesic.mathdoc.fr/item/TMF_2010_165_2_a0/

[1] P. Olver, Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | MR | MR | Zbl

[2] T. Tsujishita, Osaka J. Math., 19:2 (1982), 311–363 | MR | Zbl

[3] I. M. Anderson, “Introduction to the variational bicomplex”, Mathematical Aspects of Classical Field Theory, Contemp. Math., 132, eds. M. J. Gotay, J. E. Marsden, V. Moncrief, AMS, Providence, RI, 1992, 51–73 | DOI | MR | Zbl

[4] I. M. Anderson, The Variational Bicomplex, Dept. Math., Utah State University, Logan, Utah, 2004, 318 pp.

[5] A. Kartan, Differentsialnoe ischislenie. Differentsialnye formy, Mir, M., 1971 | MR | MR | Zbl

[6] V. V. Zharinov, TMF, 144:3 (2005), 435–452 | DOI | MR | Zbl

[7] B. Kupershmidt, Discrete Lax equations and differential-difference calculus, Astérisque, 123, SMF, Paris, 1985 | MR | Zbl

[8] P. E. Hydon, E. L. Mansfield, Found. Comput. Math., 4:2 (2004), 187–217 | DOI | MR | Zbl

[9] Ü. Göktaş, W. Hereman, Physica D, 123:1–4 (1998), 425–436, arXiv: solv-int/9801023 | DOI | MR | Zbl

[10] V. E. Adler, A. B. Shabat, R. I. Yamilov, TMF, 125:3 (2000), 355–424 | DOI | MR | Zbl

[11] E. L. Mansfield, P. E. Hydon, “On a variational complex for difference equations”, The Geometrical Study of Differential Equations, Contemp. Math., 285, eds. J. A. Leslie, T. P. Robart, AMS, Providence, RI, 2002, 121–129 | DOI | MR | Zbl

[12] M. S. Hickman, W. A. Hereman, Proc. Roy. Soc. A, 459 (2003), 2705–2729 | DOI | MR | Zbl

[13] W. Hereman, M. Colagrosso, R. Sayers, A. Ringler, B. Deconinck, M. Nivala, M. Hickman, “Continuous and discrete homotopy operators and the computation of conservation laws”, Differential Equations With Symbolic Computation, Trends Math., eds. D. Wang, Z. Zheng, Birkhäuser, Basel, 2005, 255–290 | DOI | MR | Zbl

[14] V. V. Zharinov, TMF, 157:3 (2008), 391–405 | DOI | MR | Zbl