Classification of discrete equations linearizable by point transformation on a square lattice

Christian Scimiterna; Decio Levi

doi:10.1007/s11464-013-0280-3

Front. Math. China ›› 2013, Vol. 8 ›› Issue (5) : 1067 -1076. DOI: 10.1007/s11464-013-0280-3

Research Article

RESEARCH ARTICLE

Classification of discrete equations linearizable by point transformation on a square lattice

Christian Scimiterna ¹
, Decio Levi ¹^,^b

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Abstract

We provide a complete set of linearizability conditions for nonlinear partial difference equations defined on four points and, using them, we classify all linearizable multilinear partial difference equations defined on four points up to a Möbious transformation.

Keywords

Partial difference equation / linearizable equation / point transformation

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Christian Scimiterna, Decio Levi. Classification of discrete equations linearizable by point transformation on a square lattice. Front. Math. China, 2013, 8(5): 1067-1076 DOI:10.1007/s11464-013-0280-3

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References

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[1]	Levi D, Scimiterna C. Linearizability of nonlinear equations on a quad-graph by a point, two points and generalized Hopf-Cole transformations. SIGMA, 2011, 7: 079

[2]	Levi D, Scimiterna C. Linearization through symmetries for discrete equations. arXiv: 1302.0154

[3]	Scimiterna C, Levi D. C-Integrability test for discrete equations via multiple scale expansions. SIGMA, 2010, 6: 070

[4]	Scimiterna C, Levi D. Three points partial difference equations linearizable by local and nonlocal transformations. J Phys A: Math Theor, 2013, 46: 025205