@article{SIGMA_2010_6_a91,
author = {Sergey Ya. Startsev},
title = {On {Non-Point} {Invertible} {Transformations} of {Difference} and {Differential-Difference} {Equations}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2010},
volume = {6},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a91/}
}
TY - JOUR AU - Sergey Ya. Startsev TI - On Non-Point Invertible Transformations of Difference and Differential-Difference Equations JO - Symmetry, integrability and geometry: methods and applications PY - 2010 VL - 6 UR - http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a91/ LA - en ID - SIGMA_2010_6_a91 ER -
Sergey Ya. Startsev. On Non-Point Invertible Transformations of Difference and Differential-Difference Equations. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a91/
[1] Adler V. E., Bobenko A. I., Suris Yu. B., “Classification of integrable equation on quad-graphs. The consistency approach”, Comm. Math. Phys., 233 (2003), 513–543, arXiv: nlin.SI/0202024 | DOI | MR | Zbl
[2] Theoret. and Math. Phys., 121 (1999), 1484–1495, arXiv: solv-int/9902016 | DOI | MR | Zbl
[3] Calogero F., “Why are certain nonlinear PDEs both widely applicable and integrable?”, What is integrability?, Springer Ser. Nonlinear Dynam., ed. V. E. Zakharov, Springer, Berlin, 1991, 1–62 | MR | Zbl
[4] Habibullin I. T., “Characteristic algebras of fully discrete hyperbolic type equations”, SIGMA, 1 (2005), 023, 9 pp., arXiv: nlin.SI/0506027 | DOI | MR | Zbl
[5] Habibullin I. T., Zheltukhina N., Pekcan A., “Complete list of Darboux integrable chains of the form $t_{1x}=t_x+d(t,t_1)$”, J. Math. Phys., 50 (2009), 102710, 23 pp., arXiv: 0907.3785 | DOI | MR | Zbl
[6] Hietarinta J., “A new two-dimensional lattice model that is ‘consistent around a cube’”, J. Phys. A: Math. Gen., 37 (2004), L67–L73, arXiv: nlin.SI/0311034 | DOI | MR | Zbl
[7] Hirota R., “Nonlinear partial difference equations. III. Discrete sine-Gordon equation”, J. Phys. Soc. Japan, 43 (1977), 2079–2086 | DOI | MR
[8] Hirota R., “Nonlinear partial difference equations. V. Nonlinear equations reducible to linear equations”, J. Phys. Soc. Japan, 46 (1979), 312–319 | DOI | MR
[9] Hirota R., “Discrete two-dimensional Toda molecule equation”, J. Phys. Soc. Japan, 56 (1987), 4285–4288 | DOI | MR
[10] Levi R., Yamilov R. I., “The generalized symmetry method for discrete equation”, J. Phys. A: Math. Theor., 42 (2009), 454012, 18 pp., arXiv: 0902.4421 | DOI | MR | Zbl
[11] Mikhailov A. V., Wang J. P., Xenitidis P. D., Recursion operators, conservation laws and integrability conditions for difference equations, arXiv: 1004.5346
[12] Nijhoff W. F., Quispel G. R. W., Capel H. W., “Linearization of nonlinear differential-difference equations”, Phys. Lett. A, 95 (1983), 273–276 | DOI | MR
[13] Nijhoff F. W., Capel H. W., “The discrete Korteweg–de Vries equation”, Acta Appl. Math., 39 (1995), 133–158 | DOI | MR | Zbl
[14] Orfanidis S. J., “Discrete sine-Gordon equations”, Phys. Rev. D, 18 (1978), 3822–3827 | DOI | MR
[15] Ramani A., Joshi N., Grammaticos B., Tamizhmani N., “Deconstructing an integrable lattice equation”, J. Phys. A: Math. Gen., 39 (2006), L145–L149 | DOI | MR | Zbl
[16] Sokolov V. V., Svinolupov S. I., “On nonclassical invertible transformation of hyperbolic equations”, European J. Appl. Math., 6 (1995), 145–156 | DOI | MR | Zbl
[17] Theoret. and Math. Phys., 85 (1991), 1269–1275 | DOI | MR | Zbl
[18] Yamilov R. I., “Construction scheme for discrete Miura transformation”, J. Phys. A: Math. Gen., 27 (1994), 6839–6851 | DOI | MR | Zbl
[19] Doklady Math., 52 (1996), 128–130 | MR | Zbl
[20] Russ. Math. Surv., 56:1 (2001), 61–101 | DOI | MR | Zbl