Linearizability of Nonlinear Equations on a Quad-Graph by a Point, Two Points and Generalized Hopf–Cole Transformations
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we propose some linearizability tests of partial difference equations on a quad-graph given by one point, two points and generalized Hopf–Cole transformations. We apply the so obtained tests to a set of nontrivial examples.
Keywords: quad-graph equations; linearizability; point transformations; Hopf–Cole transformations.
@article{SIGMA_2011_7_a78,
     author = {Decio Levi and Christian Scimiterna},
     title = {Linearizability of {Nonlinear} {Equations} on a {Quad-Graph} by a {Point,} {Two} {Points} and {Generalized} {Hopf{\textendash}Cole} {Transformations}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2011},
     volume = {7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a78/}
}
TY  - JOUR
AU  - Decio Levi
AU  - Christian Scimiterna
TI  - Linearizability of Nonlinear Equations on a Quad-Graph by a Point, Two Points and Generalized Hopf–Cole Transformations
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2011
VL  - 7
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a78/
LA  - en
ID  - SIGMA_2011_7_a78
ER  - 
%0 Journal Article
%A Decio Levi
%A Christian Scimiterna
%T Linearizability of Nonlinear Equations on a Quad-Graph by a Point, Two Points and Generalized Hopf–Cole Transformations
%J Symmetry, integrability and geometry: methods and applications
%D 2011
%V 7
%U http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a78/
%G en
%F SIGMA_2011_7_a78
Decio Levi; Christian Scimiterna. Linearizability of Nonlinear Equations on a Quad-Graph by a Point, Two Points and Generalized Hopf–Cole Transformations. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a78/

[1] Abel N.H., “Methode generale pour trouver des fonctions d'une seule quantite variable lorsqu'une propriete de ces fonctions est exprimee par une equation entre deux variables”, Mag. Naturvidenskab., 1 (1823), 1–10 ; reproduced in Ouvres Completes, v. I, Christiania, 1881, 1–10; Aczel J., Lectures on functional equations and their applications, Mathematics in Science and Engineering, 19, Academic Press, New York – London, 1966 | MR | MR

[2] Cole J.D., “On a quasi-linear parabolic equation occurring in aerodynamics”, Quart. Appl. Math., 9 (1951), 225–236 | MR | Zbl

[3] Hernandez Heredero R., Levi D., Scimiterna C., “A discrete linearizability test based on multiscale analysis”, J. Phys. A: Math. Theor., 43 (2010), 502002, 14 pp. ; arXiv: 1011.0141 | DOI | MR | Zbl

[4] 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

[5] Hopf E., “The partial differential equation $u_t+uu_x=u_{xx}$”, Comm. Pure Appl. Math., 3 (1950), 201–230 | DOI | MR | Zbl

[6] Levi D., Ragnisco O., Bruschi M., “Continuous and discrete matrix Burgers hierarchies”, Nuovo Cimento B, 74 (1983), 33–51 | DOI | MR

[7] Levi D., Yamilov R.I., “The generalized symmetry method for discrete equations”, J. Phys. A: Math. Theor., 42 (2009), 454012, 18 pp. ; arXiv: 0902.4421 | DOI | MR | Zbl

[8] Levi D., Yamilov R.I., “Generalized symmetry integrability test for discrete equations on the square lattice”, J. Phys. A: Math. Theor., 44 (2011), 145207, 22 pp. ; arXiv: 1011.0070 | DOI | MR | Zbl

[9] Mikhailov A.V., Wang J.P., Xenitidis P., “Recursion operators, conservation laws and integrability conditions for difference equations”, Theoret. and Math. Phys., 167 (2011), 421–443 ; arXiv: 1004.5346 | DOI

[10] Miura R.M., “Korteweg–de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation”, J. Math. Phys., 9 (1968), 1202–1204 | DOI | MR | Zbl

[11] Ramani A., Joshi N., Grammaticos B., Tamizhmani T., “Deconstructing an integrable lattice equation”, J. Phys. A: Math. Gen., 39 (2006), L145–L149 | DOI | MR | Zbl

[12] Startsev S.Ya., “On non-point invertible transformations of difference and differential-difference equations”, SIGMA, 6 (2010), 092, 14 pp. ; arXiv: 1010.0361 | DOI | MR | Zbl

[13] Uma Maheswari C., Sahadevan R., “On the conservation laws for nonlinear partial difference equations”, J. Phys. A: Math. Theor., 44 (2011), 275203, 16 pp. | DOI | Zbl