Frontiers of Mathematics in China >

2013 , Vol. 8 >Issue 5: 1067 - 1076

DOI: https://doi.org/10.1007/s11464-013-0280-3

RESEARCH ARTICLE

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

  • Christian SCIMITERNA ,
  • Decio LEVI
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  • Dipartimento di Ingegneria Elettronica, Università degli Studi Roma Tre and INFN Sezione di Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy

Received date: 31 Oct 2012

Accepted date: 10 Jan 2013

Published date: 01 Oct 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Partial Difference equation; Linearizable equation; Point transformation

Cite this article

Christian SCIMITERNA , Decio LEVI . Classification of discrete equations linearizable by point transformation on a square lattice[J]. Frontiers of Mathematics in China, 2013 , 8(5) : 1067 -1076 . DOI: 10.1007/s11464-013-0280-3

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

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