Edit Profile (opens in new tab) Levi, Decio Co-Author Distance Author ID: levi.decio Published as: Levi, D.; Levi, Decio External Links: ORCID Documents Indexed: 155 Publications since 1975, including 1 Book and 9 Additional arXiv Preprints 8 Contributions as Editor Co-Authors: 52 Co-Authors with 138 Joint Publications 1,392 Co-Co-Authors all top 5 Co-Authors 19 single-authored 45 Winternitz, Pavel 29 Scimiterna, Christian 18 Rodríguez, Miguel Angel 17 Yamilov, Ravil’ Islamovich 13 Ragnisco, Orlando 10 Petrera, Matteo 8 Thomova, Zora 6 Gubbiotti, Giorgio 6 Martina, Luigi 4 Grundland, Alfred Michel 4 Vinet, Luc 3 Nucci, Maria Clara 3 Rogers, Colin 3 Tempesta, Piergiulio 2 del Olmo, Mariano A. 2 Gegenhasi 2 Heredero, R. Hernández 2 Hu, Xingbiao 2 Negro, Javier 2 Olver, Peter John 2 Quispel, Gilles Reinout Willem 2 Sym, Antoni 2 Tremblay, Sébastien 1 Adler, Vsevolod Eduardovich 1 Atakishiev, Natig M. 1 Benguria, Rafael D. 1 Cassatella-Contra, Giovanni A. 1 Chen, Dengyuan 1 Cherdantsev, I. Yu. 1 Coley, Alan Albert 1 Dattoli, Giuseppe 1 Ferapontov, Evgeny Vladimirovich 1 Fordy, Allan P. 1 Franco, Pedro 1 Gaeta, Giuseppe 1 Garifullin, Rustem N. 1 Gómez-Ullate, David 1 Khabibullin, Ismagil Talgatovich 1 Hay, Mike C. 1 Hernández Heredero, Rafael 1 Iserles, Arieh 1 Ji, Xiaoda 1 Lattanzi, Ambra 1 Li, Yishen 1 Liu, Qingping 1 Manakov, S. V. 1 Mancinelli, Rosaria 1 Mikhailov, Alexander Vasil’evich 1 Milson, Robert 1 Moshinsky, Marcos 1 Musin, Il’dar Khamitovich 1 Nijhoff, Frank W. 1 Pilloni, L. 1 Popowicz, Ziemowit 1 Rebelo, Raphaël 1 Ricca, Eugenio 1 Sanielevici, Mihaela N. 1 Santini, Paolo Maria 1 Sekera, David 1 Shabat, Alekseĭ Borisovich 1 Sharipov, Ruslan A. 1 Sokolov, Vladimir Vyacheslavovich 1 Suleĭmanov, Bulat Irekovich 1 Torre, Amalia 1 Tsujimoto, Satoshi 1 Vinternitz, P. 1 Xue, Lingling 1 Yulmukhametov, Rinad Salavatovich 1 Zhiber, Anatoliĭ Vasil’evich all top 5 Serials 33 Journal of Physics A: Mathematical and General 26 Journal of Physics A: Mathematical and Theoretical 12 Journal of Mathematical Physics 8 Journal of Nonlinear Mathematical Physics 6 Theoretical and Mathematical Physics 6 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 4 CRM Proceedings & Lecture Notes 3 Inverse Problems 3 Ufimskiĭ Matematicheskiĭ Zhurnal 2 Studies in Applied Mathematics 1 Applicable Analysis 1 Journal of Mathematical Analysis and Applications 1 Reports on Mathematical Physics 1 Note di Matematica 1 Acta Applicandae Mathematicae 1 Physica D 1 Annals of Physics 1 Journal of Elasticity 1 Proceedings of the National Academy of Sciences of the United States of America 1 Nonlinear Analysis. Real World Applications 1 Canadian Journal of Physics 1 International Journal of Geometric Methods in Modern Physics 1 Journal of Geometry and Symmetry in Physics 1 CRM Monograph Series 1 London Mathematical Society Lecture Note Series 1 NATO ASI Series. Series B. Physics 1 Frontiers of Mathematics in China 1 Journal of Integrable Systems 1 CRM Series in Mathematical Physics all top 5 Fields 88 Partial differential equations (35-XX) 76 Difference and functional equations (39-XX) 68 Dynamical systems and ergodic theory (37-XX) 34 Ordinary differential equations (34-XX) 12 Numerical analysis (65-XX) 11 Topological groups, Lie groups (22-XX) 10 Global analysis, analysis on manifolds (58-XX) 10 Fluid mechanics (76-XX) 8 Mechanics of particles and systems (70-XX) 8 Quantum theory (81-XX) 7 General and overarching topics; collections (00-XX) 5 Nonassociative rings and algebras (17-XX) 3 Differential geometry (53-XX) 2 History and biography (01-XX) 2 Special functions (33-XX) 1 Combinatorics (05-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Operator theory (47-XX) 1 Mechanics of deformable solids (74-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 118 Publications have been cited 1,019 times in 657 Documents Cited by ▼ Year ▼ Non-classical symmetry reduction: Example of the Boussinesq equation. Zbl 0694.35159 Levi, D.; Winternitz, P. 115 1989 Symmetry reduction for the Kadomtsev-Petviashvili equation using a loop algebra. Zbl 0598.35117 David, D.; Kamran, N.; Levi, D.; Winternitz, P. 66 1986 Bäcklund transformations and nonlinear differential difference equations. Zbl 0453.35072 Levi, D.; Benguria, R. 44 1980 Nonlinear differential difference equations as Bäcklund transformations. Zbl 0465.35081 Levi, D. 39 1981 Continuous symmetries of difference equations. Zbl 1112.37053 Levi, Decio; Winternitz, Pavel 34 2006 Conditions for the existence of higher symmetries of evolutionary equations on the lattice. Zbl 0896.34057 Levi, D.; Yamilov, R. 31 1997 Lie group formalism for difference equations. Zbl 0956.39013 Levi, D.; Vinet, L.; Winternitz, P. 31 1997 Symmetries and conditional symmetries of differential-difference equations. Zbl 0780.34047 Levi, D.; Winternitz, P. 28 1993 The nonabelian Toda lattice - Discrete analogue of the matrix Schrödinger spectral problem. Zbl 0451.35054 Bruschi, M.; Manakov, S. V.; Ragnisco, O.; Levi, D. 26 1980 Symmetries of discrete dynamical systems. Zbl 0862.34049 Levi, D.; Winternitz, P. 22 1996 On non-isospectral flows, Painlevé equations, and symmetries of differential and difference equations. Zbl 0801.35122 Levi, D.; Ragnisco, O.; Rodriguez, M. A. 21 1992 A hierarchy of coupled Korteweg-de Vries equations and the normalization conditions of the Hilbert-Riemann problem. Zbl 0548.35098 Levi, D.; Sym, A.; Wojciechowski, S. 20 1983 On a new Darboux transformation for the construction of exact solutions of the Schrödinger equation. Zbl 0701.34036 Levi, D. 20 1988 Non-isospectral deformations and Darboux transformations for the third- order spectral problem. Zbl 0694.35211 Levi, D.; Ragnisco, O. 19 1988 Integrable nonlinear equations for water waves in straits of varying depth and width. Zbl 0678.35008 David, D.; Levi, D.; Winternitz, P. 18 1987 The Kundu-Eckhaus equation and its discretizations. Zbl 1181.35243 Levi, Decio; Scimiterna, Christian 18 2009 Generalized symmetry integrability test for discrete equations on the square lattice. Zbl 1225.37079 Levi, D.; Yamilov, R. I. 17 2011 Evolution equations associated with the discrete analog of the matrix Schrödinger spectral problem solvable by the inverse spectral transform. Zbl 0513.35026 Bruschi, M.; Ragnisco, O.; Levi, D. 16 1981 The generalized symmetry method for discrete equations. Zbl 1180.37093 Levi, D.; Yamilov, R. I. 16 2009 Umbral calculus, difference equations and the discrete Schrödinger equation. Zbl 1064.39020 Levi, Decio; Tempesta, Piergiulio; Winternitz, Pavel 16 2004 Solitons in shallow seas of variable depth and in marine straits. Zbl 0728.76023 David, D.; Levi, D.; Winternitz, P. 15 1989 Integrable three-dimensional lattices. Zbl 0481.35046 Levi, D.; Pilloni, L.; Santini, P. M. 14 1981 Group theoretical analysis of a rotating shallow liquid in a rigid container. Zbl 0715.35067 Levi, D.; Nucci, M. C.; Rogers, C.; Winternitz, P. 14 1989 On higher-order Riccati equations as Bäcklund transformations. Zbl 0937.35161 Grundland, A. M.; Levi, D. 13 1999 Supersymmetric KdV equation: Darboux transformation and discrete systems. Zbl 1286.35224 Xue, Ling-Ling; Levi, D.; Liu, Q. P. 13 2013 Classification of five-point differential-difference equations. Zbl 1376.34016 Garifullin, R. N.; Yamilov, R. I.; Levi, D. 12 2017 Symmetries of the discrete Burgers equation. Zbl 0941.35093 Hernández Heredero, R.; Levi, D.; Winternitz, P. 11 1999 Lie algebra contractions and symmetries of the Toda hierarchy. Zbl 0973.37046 Hernández Heredero, R.; Levi, D.; Rodríguez, M. A.; Winternitz, P. 11 2000 Lie point symmetries of difference equations and lattices. Zbl 0966.39007 Levi, D.; Tremblay, S.; Winternitz, P. 11 2000 Heisenberg algebra, umbral calculus and orthogonal polynomials. Zbl 1152.81396 Dattoli, G.; Levi, D.; Winternitz, P. 11 2008 Integrable hierarchies of nonlinear difference-difference equations and symmetries. Zbl 1003.39011 Levi, D.; Martina, L. 9 2001 On the integrability of a new lattice equation found by multiple scale analysis. Zbl 1293.35355 Scimiterna, Christian; Hay, Mike; Levi, Decio 9 2014 Structure preserving discretizations of the Liouville equation and their numerical tests. Zbl 1358.35072 Levi, Decio; Martina, Luigi; Winternitz, Pavel 9 2015 Non-invertible transformations of differential-difference equations. Zbl 1378.37116 Garifullin, R. N.; Yamilov, R. I.; Levi, D. 9 2016 \(\lambda \)-symmetries and Jacobi last multiplier. Zbl 1266.34058 Nucci, M. C.; Levi, D. 9 2013 Algebraic entropy, symmetries and linearization of quad equations consistent on the cube. Zbl 1420.37064 Gubbiotti, G.; Scimiterna, C.; Levi, D. 9 2016 Lie symmetries of multidimensional difference equations. Zbl 0998.39008 Levi, D.; Tremblay, S.; Winternitz, P. 8 2001 Discrete \(q\)-derivatives and symmetries of \(q\)-difference equations. Zbl 1056.81042 Levi, D.; Negro, J.; del Olmo, M. A. 8 2004 On Miura transformations and Volterra-type equations associated with the Adler-Bobenko-Suris equations. Zbl 1168.37019 Levi, Decio; Petrera, Matteo; Scimiterna, Christian; Yamilov, Ravil 8 2008 Lie-point symmetries of the discrete Liouville equation. Zbl 1315.37042 Levi, D.; Martina, L.; Winternitz, P. 8 2015 The non-autonomous YdKN equation and generalized symmetries of Boll equations. Zbl 1367.34002 Gubbiotti, G.; Scimiterna, C.; Levi, D. 8 2017 Classification of five-point differential-difference equations. II. Zbl 1386.34019 Garifullin, R. N.; Yamilov, R. I.; Levi, D. 7 2018 Symmetries of the continuous and discrete Krichever-Novikov equation. Zbl 1244.35004 Levi, Decio; Winternitz, Pavel; Yamilov, Ravil I. 7 2011 Lie point symmetries of differential-difference equations. Zbl 1197.35303 Levi, D.; Winternitz, P.; Yamilov, R. I. 7 2010 On a nonlinear integrable difference equation on the square. Zbl 1240.39020 Levi, D.; Yamilov, R. I. 6 2009 Discrete third-order spectral problems and a new Toda-type equation. Zbl 1004.37050 Levi, D.; Grundland, A. M. 6 2002 Linearizability and a fake Lax pair for a nonlinear nonautonomous quad-graph equation consistent around the cube. Zbl 1359.37132 Gubbiotti, G.; Scimiterna, C.; Levi, Decio 6 2016 Multiple-scale analysis of discrete nonlinear partial difference equations: The reduction of the lattice potential KdV. Zbl 1082.39013 Levi, D. 5 2005 Symmetries and integrability of difference equations. Papers from the workshop, May 22–29, 1994, Estérel, Canada. Zbl 0852.00027 5 1996 Linearizability of nonlinear equations on a quad-graph by a point, two points and generalized Hopf-Cole transformations. Zbl 1245.39010 Levi, Decio; Scimiterna, Christian 5 2011 \(\lambda\)-symmetries for the reduction of continuous and discrete equations. Zbl 1267.34061 Levi, D.; Nucci, M. C.; Rodríguez, M. A. 5 2012 Discrete reductive perturbation technique. Zbl 1111.39016 Levi, Decio; Petrera, Matteo 4 2006 Multiscale expansion of the lattice potential KdV equation on functions of an infinite slow-varyness order. Zbl 1149.35073 Hernandez Heredero, R.; Levi, D.; Petrera, M.; Scimiterna, C. 4 2007 The lattice Schwarzian KdV equation and its symmetries. Zbl 1155.35438 Levi, D.; Petrera, M.; Scimiterna, C. 4 2007 Levi-Civita theory for irrotational water waves in a one-dimensional channel and the complex Korteweg-de Vries equation. Zbl 0853.76008 Levi, D. 4 1994 Toward a unification of the various techniques used to integrate nonlinear partial differential equations: Bäcklund and Darboux transformations vs. dressing method. Zbl 0621.35095 Levi, Decio 4 1986 Lie point symmetries and commuting flows for equations on lattices. Zbl 1215.39008 Levi, D.; Winternitz, P. 4 2002 \(\lambda \)-symmetries for discrete equations. Zbl 1262.39001 Levi, D.; Rodríguez, M. A. 4 2010 Differential equations invariant under conditional symmetries. Zbl 1462.35337 Levi, Decio; Rodríguez, Miguel A.; Thomova, Zora 4 2019 Continuous symmetries of the lattice potential KdV equation. Zbl 1115.35111 Levi, Decio; Petrera, Matteo 3 2007 Integrability test of discrete nonlinear Schrödinger equations via multiscale reduction. Zbl 1189.39008 Levi, Decio; Scimiterna, Christian 3 2010 SIDE III – Symmetries and integrability of difference equations. Proceedings of the 3rd conference, Sabaudia, Italy, May 16–22, 1998. Zbl 0943.00052 3 2000 Discrete derivatives and symmetries of difference equations. Zbl 0974.39007 Levi, D.; Negro, J.; del Olmo, M. A. 3 2001 The inhomogeneous Toda lattice: Its hierarchy and Darboux-Bäcklund transformations. Zbl 0734.35136 Levi, D.; Ragnisco, O. 3 1991 Lie point symmetries of differential difference equations. Zbl 0860.22016 Levi, Decio; Winternitz, Pavel 3 1996 Toda lattice and generalised Wronskian technique. Zbl 0445.35011 Bruschi, M.; Levi, D.; Ragnisco, O. 3 1980 Multiscale expansion on the lattice and integrability of partial difference equations. Zbl 1143.37046 Hernandez Heredero, R.; Levi, D.; Petrera, M.; Scimiterna, C. 3 2008 A two-periodic generalization of the \(Q_V\) equation. Zbl 1398.39007 Gubbiotti, G.; Scimiterna, C.; Levi, D. 3 2017 Linearization through symmetries for discrete equations. Zbl 1276.39003 Levi, D.; Scimiterna, C. 3 2013 Symmetries and integrability of difference equations. Based upon lectures delivered during the summer school, Montreal, Canada, June 8–21, 2008. Zbl 1218.39002 3 2011 Three-point partial difference equations linearizable by local and nonlocal transformations. Zbl 1266.39013 Scimiterna, C.; Levi, D. 3 2012 Non-linear differential-difference equations with N-dependent coefficients. II. Zbl 0477.34047 Levi, D.; Ragnisco, O. 2 1979 Some remarks on the normalisation condition problem of dressing method. Zbl 0542.35080 Levi, D.; Ragnisco, O.; Sym, A. 2 1984 Painlevé transcendents: their asymptotics and physical applications. Proceedings of the NATO Advanced Research Workshop, Sainte-Adèle, Canada, September 3-7, 1990. Zbl 0846.00007 2 1992 Generalized Lie symmetries for difference equations. Zbl 1229.39002 Levi, Decio; Yamilov, Ravil I. 2 2011 Symmetry preserving discretization of the Burgers equation. Zbl 0963.35168 Hernández Heredero, R.; Levi, D.; Winternitz, P. 2 2000 Construction of higher local \((2+1)\)-dimensional exponential lattice equations. Zbl 0991.37541 Levi, D.; Ragnisco, O.; Shabat, A. B. 2 1994 Lie symmetries for integrable evolution equations on the lattice. Zbl 0955.37050 Levi, D.; Rodríguez, M. A. 2 1999 Symmetries of the discrete nonlinear Schrödinger equation. Zbl 1002.39031 Hernández Heredero, R.; Levi, D.; Winternitz, P. 2 2001 Integrability conditions for \(n\) and \(t\) dependent dynamical lattice equations. Zbl 1161.37345 Yamilov, R.; Levi, D. 2 2004 Lie discrete symmetries of lattice equations. Zbl 1052.39500 Levi, Decio; Rodríguez, Miguel A. 2 2004 Equivalence of a class of Wigner coefficients of SU(1,1) with those of SU(2). Zbl 0306.20053 Chacon, E.; Levi, D.; Moshinsky, M. 2 1975 Symmetries and nonlinear phenomena. Proceedings of the international school on applied mathematics, Paipa, Colombia, Feb. 22-26, 1988. Zbl 0747.00041 2 1988 Symmetry group of partial differential equations and of differential difference equations: The Toda lattice versus the Korteweg-de Vries equation. Zbl 0754.35144 Levi, D.; Rodríguez, M. A. 2 1992 Irrotational water waves and the complex Korteweg-de Vries equation. Zbl 0899.76083 Levi, D.; Sanielevici, M. 2 1996 Conformally invariant elliptic Liouville equation and its symmetry-preserving discretization. Zbl 1409.35087 Levi, D.; Martina, L.; Winternitz, P. 2 2018 Construction of partial difference schemes: I. The Clairaut, Schwarz, Young theorem on the lattice. Zbl 1273.65161 Levi, Decio; Rodríguez, Miguel A. 2 2013 A discrete linearizability test based on multiscale analysis. Zbl 1208.39010 Hernández Heredero, R.; Levi, D.; Scimiterna, C. 2 2010 The discretized Boussinesq equation and its conditional symmetry reduction. Zbl 1511.39014 Levi, Decio; Rodríguez, Miguel A.; Thomova, Zora 2 2020 Lie point symmetries and ODEs passing the Painlevé test. Zbl 1417.34211 Levi, D.; Sekera, D.; Winternitz, P. 2 2018 Four points linearizable lattice schemes. Zbl 1288.35022 Levi, Decio; Scimiterna, Christian 2 2013 Continuous symmetries of differential-difference equations. Zbl 1102.35366 Winternitz, P.; Levi, D. 1 1995 Contact transformations for difference schemes. Zbl 1239.65054 Levi, Decio; Scimiterna, Christian; Thomova, Zora; Winternitz, Pavel 1 2012 Are there contact transformations for discrete equations? Zbl 1227.39002 Levi, Decio; Thomova, Zora; Winternitz, Pavel 1 2011 On a discrete Davey–Stewartson system. Zbl 1106.35093 Gegenhasi; Hu, Xing-Biao; Levi, Decio 1 2006 Symmetries of discrete physical systems. Zbl 0948.37501 Levi, D.; Vinet, L.; Winternitz, P. 1 1996 Bäcklund and Darboux transformations. The geometry of solitons. AARMS-CRM workshop, Halifax, Canada, June 4–9, 1999. With short biographies of Albert Victor Bäcklund and Gaston Darboux. Zbl 0974.00040 1 2001 Lie symmetries for lattice equations. Zbl 1195.37048 Levi, Decio 1 2005 On strong and weak Bäcklund transformations. Zbl 0586.35019 Levi, D.; Popowicz, Z. 1 1985 Kadomtsev-Petviashvili equations in the description of water waves. Zbl 0726.76019 Levi, D. 1 1990 Continuous symmetries and integrability of discrete equations. Zbl 1525.39001 Levi, Decio; Winternitz, Pavel; Yamilov, Ravil I. 1 2022 Yamilov’s theorem for differential and difference equations. Zbl 1488.39050 Levi, Decio; Rodríguez, Miguel A. 1 2021 The discretized Boussinesq equation and its conditional symmetry reduction. Zbl 1511.39014 Levi, Decio; Rodríguez, Miguel A.; Thomova, Zora 2 2020 Differential equations invariant under conditional symmetries. Zbl 1462.35337 Levi, Decio; Rodríguez, Miguel A.; Thomova, Zora 4 2019 Construction of partial differential equations with conditional symmetries. Zbl 1425.35156 Levi, Decio; Rodríguez, Miguel A.; Thomova, Zora 1 2019 Classification of five-point differential-difference equations. II. Zbl 1386.34019 Garifullin, R. N.; Yamilov, R. I.; Levi, D. 7 2018 Conformally invariant elliptic Liouville equation and its symmetry-preserving discretization. Zbl 1409.35087 Levi, D.; Martina, L.; Winternitz, P. 2 2018 Lie point symmetries and ODEs passing the Painlevé test. Zbl 1417.34211 Levi, D.; Sekera, D.; Winternitz, P. 2 2018 Time-dependent free-particle Salpeter equation: features of the solutions. Zbl 1406.81041 Torre, Amalia; Lattanzi, Ambra; Levi, Decio 1 2018 Classification of five-point differential-difference equations. Zbl 1376.34016 Garifullin, R. N.; Yamilov, R. I.; Levi, D. 12 2017 The non-autonomous YdKN equation and generalized symmetries of Boll equations. Zbl 1367.34002 Gubbiotti, G.; Scimiterna, C.; Levi, D. 8 2017 A two-periodic generalization of the \(Q_V\) equation. Zbl 1398.39007 Gubbiotti, G.; Scimiterna, C.; Levi, D. 3 2017 Non-invertible transformations of differential-difference equations. Zbl 1378.37116 Garifullin, R. N.; Yamilov, R. I.; Levi, D. 9 2016 Algebraic entropy, symmetries and linearization of quad equations consistent on the cube. Zbl 1420.37064 Gubbiotti, G.; Scimiterna, C.; Levi, D. 9 2016 Linearizability and a fake Lax pair for a nonlinear nonautonomous quad-graph equation consistent around the cube. Zbl 1359.37132 Gubbiotti, G.; Scimiterna, C.; Levi, Decio 6 2016 Structure preserving discretizations of the Liouville equation and their numerical tests. Zbl 1358.35072 Levi, Decio; Martina, Luigi; Winternitz, Pavel 9 2015 Lie-point symmetries of the discrete Liouville equation. Zbl 1315.37042 Levi, D.; Martina, L.; Winternitz, P. 8 2015 On the integrability of a new lattice equation found by multiple scale analysis. Zbl 1293.35355 Scimiterna, Christian; Hay, Mike; Levi, Decio 9 2014 Lie group analysis of a generalized Krichever-Novikov differential-difference equation. Zbl 1366.39015 Levi, Decio; Ricca, Eugenio; Thomova, Zora; Winternitz, Pavel 1 2014 Supersymmetric KdV equation: Darboux transformation and discrete systems. Zbl 1286.35224 Xue, Ling-Ling; Levi, D.; Liu, Q. P. 13 2013 \(\lambda \)-symmetries and Jacobi last multiplier. Zbl 1266.34058 Nucci, M. C.; Levi, D. 9 2013 Linearization through symmetries for discrete equations. Zbl 1276.39003 Levi, D.; Scimiterna, C. 3 2013 Construction of partial difference schemes: I. The Clairaut, Schwarz, Young theorem on the lattice. Zbl 1273.65161 Levi, Decio; Rodríguez, Miguel A. 2 2013 Four points linearizable lattice schemes. Zbl 1288.35022 Levi, Decio; Scimiterna, Christian 2 2013 Classification of discrete equations linearizable by point transformation on a square lattice. Zbl 1279.39006 Scimiterna, Christian; Levi, Decio 1 2013 \(\lambda\)-symmetries for the reduction of continuous and discrete equations. Zbl 1267.34061 Levi, D.; Nucci, M. C.; Rodríguez, M. A. 5 2012 Three-point partial difference equations linearizable by local and nonlocal transformations. Zbl 1266.39013 Scimiterna, C.; Levi, D. 3 2012 Contact transformations for difference schemes. Zbl 1239.65054 Levi, Decio; Scimiterna, Christian; Thomova, Zora; Winternitz, Pavel 1 2012 On Fourier integral transforms for \(q\)-Fibonacci and \(q\)-Lucas polynomials. Zbl 1248.33031 Atakishiyev, Natig; Franco, Pedro; Levi, Decio; Ragnisco, Orlando 1 2012 The Jacobi last multiplier for linear partial difference equations. Zbl 1247.39009 Levi, Decio; Rodríguez, Miguel A. 1 2012 Generalized symmetry integrability test for discrete equations on the square lattice. Zbl 1225.37079 Levi, D.; Yamilov, R. I. 17 2011 Symmetries of the continuous and discrete Krichever-Novikov equation. Zbl 1244.35004 Levi, Decio; Winternitz, Pavel; Yamilov, Ravil I. 7 2011 Linearizability of nonlinear equations on a quad-graph by a point, two points and generalized Hopf-Cole transformations. Zbl 1245.39010 Levi, Decio; Scimiterna, Christian 5 2011 Symmetries and integrability of difference equations. Based upon lectures delivered during the summer school, Montreal, Canada, June 8–21, 2008. Zbl 1218.39002 3 2011 Generalized Lie symmetries for difference equations. Zbl 1229.39002 Levi, Decio; Yamilov, Ravil I. 2 2011 Are there contact transformations for discrete equations? Zbl 1227.39002 Levi, Decio; Thomova, Zora; Winternitz, Pavel 1 2011 Lie point symmetries of differential-difference equations. Zbl 1197.35303 Levi, D.; Winternitz, P.; Yamilov, R. I. 7 2010 \(\lambda \)-symmetries for discrete equations. Zbl 1262.39001 Levi, D.; Rodríguez, M. A. 4 2010 Integrability test of discrete nonlinear Schrödinger equations via multiscale reduction. Zbl 1189.39008 Levi, Decio; Scimiterna, Christian 3 2010 A discrete linearizability test based on multiscale analysis. Zbl 1208.39010 Hernández Heredero, R.; Levi, D.; Scimiterna, C. 2 2010 \(C\)-integrability test for discrete equations via multiple scale expansions. Zbl 1219.39002 Scimiterna, Christian; Levi, Decio 1 2010 Discrete multiscale analysis: a biatomic lattice system. Zbl 1203.35260 Cassatella Contra, G. A.; Levi, D. 1 2010 The Kundu-Eckhaus equation and its discretizations. Zbl 1181.35243 Levi, Decio; Scimiterna, Christian 18 2009 The generalized symmetry method for discrete equations. Zbl 1180.37093 Levi, D.; Yamilov, R. I. 16 2009 On a nonlinear integrable difference equation on the square. Zbl 1240.39020 Levi, D.; Yamilov, R. I. 6 2009 Heisenberg algebra, umbral calculus and orthogonal polynomials. Zbl 1152.81396 Dattoli, G.; Levi, D.; Winternitz, P. 11 2008 On Miura transformations and Volterra-type equations associated with the Adler-Bobenko-Suris equations. Zbl 1168.37019 Levi, Decio; Petrera, Matteo; Scimiterna, Christian; Yamilov, Ravil 8 2008 Multiscale expansion on the lattice and integrability of partial difference equations. Zbl 1143.37046 Hernandez Heredero, R.; Levi, D.; Petrera, M.; Scimiterna, C. 3 2008 Multiscale expansion and integrability properties of the lattice potential KdV equation. Zbl 1362.35262 Hernandez Heredero, Rafael; Levi, Decio; Petrera, Matteo; Scimiterna, Christian 1 2008 Multiscale expansion of the lattice potential KdV equation on functions of an infinite slow-varyness order. Zbl 1149.35073 Hernandez Heredero, R.; Levi, D.; Petrera, M.; Scimiterna, C. 4 2007 The lattice Schwarzian KdV equation and its symmetries. Zbl 1155.35438 Levi, D.; Petrera, M.; Scimiterna, C. 4 2007 Continuous symmetries of the lattice potential KdV equation. Zbl 1115.35111 Levi, Decio; Petrera, Matteo 3 2007 Continuous symmetries of difference equations. Zbl 1112.37053 Levi, Decio; Winternitz, Pavel 34 2006 Discrete reductive perturbation technique. Zbl 1111.39016 Levi, Decio; Petrera, Matteo 4 2006 On a discrete Davey–Stewartson system. Zbl 1106.35093 Gegenhasi; Hu, Xing-Biao; Levi, Decio 1 2006 Multiple-scale analysis of discrete nonlinear partial difference equations: The reduction of the lattice potential KdV. Zbl 1082.39013 Levi, D. 5 2005 Lie symmetries for lattice equations. Zbl 1195.37048 Levi, Decio 1 2005 Asymptotic symmetries of difference equations on a lattice. Zbl 1126.39300 Gaeta, Giuseppe; Levi, Decio; Mancinelli, Rosaria 1 2005 Umbral calculus, difference equations and the discrete Schrödinger equation. Zbl 1064.39020 Levi, Decio; Tempesta, Piergiulio; Winternitz, Pavel 16 2004 Discrete \(q\)-derivatives and symmetries of \(q\)-difference equations. Zbl 1056.81042 Levi, D.; Negro, J.; del Olmo, M. A. 8 2004 Integrability conditions for \(n\) and \(t\) dependent dynamical lattice equations. Zbl 1161.37345 Yamilov, R.; Levi, D. 2 2004 Lie discrete symmetries of lattice equations. Zbl 1052.39500 Levi, Decio; Rodríguez, Miguel A. 2 2004 The discrete nonlinear Schrödinger equation and its Lie symmetry reductions. Zbl 1362.39010 Hernández Heredero, R.; Levi, D. 1 2003 On a discrete version of the \(\mathbb CP^1\) sigma model and surfaces immersed in \(\mathbb R^3\). Zbl 1057.53004 Grundland, A. M.; Levi, D.; Martina, L. 1 2003 Discrete third-order spectral problems and a new Toda-type equation. Zbl 1004.37050 Levi, D.; Grundland, A. M. 6 2002 Lie point symmetries and commuting flows for equations on lattices. Zbl 1215.39008 Levi, D.; Winternitz, P. 4 2002 Integrable hierarchies of nonlinear difference-difference equations and symmetries. Zbl 1003.39011 Levi, D.; Martina, L. 9 2001 Lie symmetries of multidimensional difference equations. Zbl 0998.39008 Levi, D.; Tremblay, S.; Winternitz, P. 8 2001 Discrete derivatives and symmetries of difference equations. Zbl 0974.39007 Levi, D.; Negro, J.; del Olmo, M. A. 3 2001 Symmetries of the discrete nonlinear Schrödinger equation. Zbl 1002.39031 Hernández Heredero, R.; Levi, D.; Winternitz, P. 2 2001 Bäcklund and Darboux transformations. The geometry of solitons. AARMS-CRM workshop, Halifax, Canada, June 4–9, 1999. With short biographies of Albert Victor Bäcklund and Gaston Darboux. Zbl 0974.00040 1 2001 Lie algebra contractions and symmetries of the Toda hierarchy. Zbl 0973.37046 Hernández Heredero, R.; Levi, D.; Rodríguez, M. A.; Winternitz, P. 11 2000 Lie point symmetries of difference equations and lattices. Zbl 0966.39007 Levi, D.; Tremblay, S.; Winternitz, P. 11 2000 SIDE III – Symmetries and integrability of difference equations. Proceedings of the 3rd conference, Sabaudia, Italy, May 16–22, 1998. Zbl 0943.00052 3 2000 Symmetry preserving discretization of the Burgers equation. Zbl 0963.35168 Hernández Heredero, R.; Levi, D.; Winternitz, P. 2 2000 On higher-order Riccati equations as Bäcklund transformations. Zbl 0937.35161 Grundland, A. M.; Levi, D. 13 1999 Symmetries of the discrete Burgers equation. Zbl 0941.35093 Hernández Heredero, R.; Levi, D.; Winternitz, P. 11 1999 Lie symmetries for integrable evolution equations on the lattice. Zbl 0955.37050 Levi, D.; Rodríguez, M. A. 2 1999 Conditions for the existence of higher symmetries of evolutionary equations on the lattice. Zbl 0896.34057 Levi, D.; Yamilov, R. 31 1997 Lie group formalism for difference equations. Zbl 0956.39013 Levi, D.; Vinet, L.; Winternitz, P. 31 1997 Symmetries of discrete dynamical systems. Zbl 0862.34049 Levi, D.; Winternitz, P. 22 1996 Symmetries and integrability of difference equations. Papers from the workshop, May 22–29, 1994, Estérel, Canada. Zbl 0852.00027 5 1996 Lie point symmetries of differential difference equations. Zbl 0860.22016 Levi, Decio; Winternitz, Pavel 3 1996 Irrotational water waves and the complex Korteweg-de Vries equation. Zbl 0899.76083 Levi, D.; Sanielevici, M. 2 1996 Symmetries of discrete physical systems. Zbl 0948.37501 Levi, D.; Vinet, L.; Winternitz, P. 1 1996 Continuous symmetries of differential-difference equations. Zbl 1102.35366 Winternitz, P.; Levi, D. 1 1995 Levi-Civita theory for irrotational water waves in a one-dimensional channel and the complex Korteweg-de Vries equation. Zbl 0853.76008 Levi, D. 4 1994 Construction of higher local \((2+1)\)-dimensional exponential lattice equations. Zbl 0991.37541 Levi, D.; Ragnisco, O.; Shabat, A. B. 2 1994 Symmetries and conditional symmetries of a non-relativistic Chern-Simons system. Zbl 0793.35101 Levi, Decio; Vinet, Luc; Winternitz, Pavel 1 1994 Symmetries and conditional symmetries of differential-difference equations. Zbl 0780.34047 Levi, D.; Winternitz, P. 28 1993 Dimensional reduction for equations involving discrete and continuous variables. Zbl 0793.35105 Levi, D.; Winternitz, P. 1 1993 On non-isospectral flows, Painlevé equations, and symmetries of differential and difference equations. Zbl 0801.35122 Levi, D.; Ragnisco, O.; Rodriguez, M. A. 21 1992 Painlevé transcendents: their asymptotics and physical applications. Proceedings of the NATO Advanced Research Workshop, Sainte-Adèle, Canada, September 3-7, 1990. Zbl 0846.00007 2 1992 Symmetry group of partial differential equations and of differential difference equations: The Toda lattice versus the Korteweg-de Vries equation. Zbl 0754.35144 Levi, D.; Rodríguez, M. A. 2 1992 Symmetry reduction for the stimulated Raman scattering equations and the asymptotics of Painleve’ \(V\) via Boutroux transformation. Zbl 0875.35125 Levi, D. 1 1992 The inhomogeneous Toda lattice: Its hierarchy and Darboux-Bäcklund transformations. Zbl 0734.35136 Levi, D.; Ragnisco, O. 3 1991 Kadomtsev-Petviashvili equations in the description of water waves. Zbl 0726.76019 Levi, D. 1 1990 Group invariance of a neo-Hookean system: Incorporation of stretch change. Zbl 0733.73020 Levi, D.; Rogers, C. 1 1990 Non-classical symmetry reduction: Example of the Boussinesq equation. Zbl 0694.35159 Levi, D.; Winternitz, P. 115 1989 Solitons in shallow seas of variable depth and in marine straits. Zbl 0728.76023 David, D.; Levi, D.; Winternitz, P. 15 1989 ...and 18 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 751 Authors 31 Levi, Decio 29 Winternitz, Pavel 16 Yamilov, Ravil’ Islamovich 15 Folly-Gbetoula, Mensah K. 14 Clarkson, Peter A. 14 Gordoa, Pilar Ruiz 13 Pickering, Andrew 12 Dorodnitsyn, Vladimir A. 12 Gubbiotti, Giorgio 11 Zhang, Dajun 10 Adler, Vsevolod Eduardovich 10 Güngör, Faruk 10 Lou, Senyue 10 Sahadevan, Ramajayam 10 Scimiterna, Christian 9 Khabibullin, Ismagil Talgatovich 9 Liu, Qingping 9 Meleshko, Sergey V. 9 Nyirenda, Darlison 9 Tam, Hon-Wah 8 Doliwa, Adam 8 Geng, Xianguo 8 Hu, Xingbiao 8 Mikhailov, Alexander Vasil’evich 8 Santini, Paolo Maria 7 Kozlov, Roman V. 7 Mao, Hui 7 Rodríguez, Miguel Angel 7 Zhang, Yingnan 6 Cieśliński, Jan L. 6 Kim, Dae San 6 Kim, Taekyun 6 Popovych, Roman O. 6 Thomova, Zora 6 Tian, Bo 6 Xenitidis, Pavlos 6 Zhang, Yufeng 6 Zhu, Zuonong 5 Cariñena, José F. 5 Fan, Engui 5 Gaeta, Giuseppe 5 Grundland, Alfred Michel 5 Kara, Abdul Hamid 5 Konstantinou-Rizos, Sotiris 5 Ma, Wen-Xiu 5 Mansour, Toufik 5 Ragnisco, Orlando 5 Sophocleous, Christodoulos 5 Tian, Shoufu 5 Valiquette, Francis 5 Wang, Jingping 5 Xue, Lingling 5 Zhdanov, Renat Z. 4 Bihlo, Alexander 4 Chen, Yong 4 Cherniha, Roman M. 4 Cicogna, Giampaolo 4 de Lucas, Javier 4 Dolgiĭ, Dmitriĭ Viktorovich 4 Dong, Huanhe 4 Gekhtman, Mikhaèl I. 4 Grammaticos, Basil 4 He, Guoliang 4 Huang, Dingjiang 4 Ji, Lina 4 Nucci, Maria Clara 4 Rogers, Colin 4 Shabat, Alekseĭ Borisovich 4 Shen, Shoufeng 4 Tempesta, Piergiulio 4 van der Kamp, Peter H. 4 Xue, Bo 4 Zhang, Hongqing 3 Arrigo, Daniel J. 3 Berezans’kyĭ, Yuriĭ Makarovych 3 Broadbridge, Philip 3 Cao, Cewen 3 Dattoli, Giuseppe 3 Kaptsov, Evgeniy I. 3 Karsli, Harun 3 Khan, Subuhi 3 Li, Biao 3 Li, Juan 3 Li, Nianhua 3 Mansfield, Elizabeth Louise 3 Marín, María José 3 Medina, Elena 3 Ndogmo, Jean-Claude 3 Nieszporski, Maciej 3 Nijhoff, Frank W. 3 Qiao, Zhijun 3 Qu, Changzheng 3 Ramani, Alfred 3 Rebelo, Raphaël 3 Senthilvelan, Murugaian 3 Sun, Jianqing 3 Tian, Kai 3 Tran, Dinh Thi 3 Tsyfra, Ivan M. 3 Vakhnenko, Oleksiy O. ...and 651 more Authors all top 5 Cited in 141 Serials 115 Journal of Mathematical Physics 39 Journal of Nonlinear Mathematical Physics 32 Theoretical and Mathematical Physics 31 Journal of Mathematical Analysis and Applications 30 Journal of Physics A: Mathematical and Theoretical 25 Communications in Nonlinear Science and Numerical Simulation 23 Applied Mathematics and Computation 18 Chaos, Solitons and Fractals 14 Physics Letters. 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Mathematical, Physical and Engineering Sciences 2 Mathematical Foundations of Computing 1 Applicable Analysis 1 European Journal of Physics 1 Geophysical and Astrophysical Fluid Dynamics 1 General Relativity and Gravitation 1 International Journal of Control 1 International Journal of Theoretical Physics 1 Linear and Multilinear Algebra 1 Nuclear Physics. B 1 Physics Reports 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Physics of Fluids, A 1 Mathematics of Computation 1 BIT 1 Mathematics and Computers in Simulation 1 Mathematische Nachrichten 1 Proceedings of the American Mathematical Society 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Results in Mathematics 1 Ricerche di Matematica 1 Transactions of the American Mathematical Society 1 Advances in Applied Mathematics 1 Chinese Annals of Mathematics. Series B 1 Applied Numerical Mathematics 1 Probability Theory and Related Fields 1 Science in China. Series A 1 Numerical Algorithms 1 Applied Mathematical Modelling ...and 41 more Serials all top 5 Cited in 49 Fields 352 Partial differential equations (35-XX) 320 Dynamical systems and ergodic theory (37-XX) 134 Difference and functional equations (39-XX) 90 Ordinary differential equations (34-XX) 57 Global analysis, analysis on manifolds (58-XX) 51 Fluid mechanics (76-XX) 40 Quantum theory (81-XX) 34 Numerical analysis (65-XX) 32 Mechanics of particles and systems (70-XX) 29 Nonassociative rings and algebras (17-XX) 29 Special functions (33-XX) 16 Differential geometry (53-XX) 14 Combinatorics (05-XX) 10 Topological groups, Lie groups (22-XX) 10 Optics, electromagnetic theory (78-XX) 10 Biology and other natural sciences (92-XX) 9 Number theory (11-XX) 8 Computer science (68-XX) 8 Mechanics of deformable solids (74-XX) 8 Relativity and gravitational theory (83-XX) 7 Operator theory (47-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 Associative rings and algebras (16-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Functions of a complex variable (30-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Probability theory and stochastic processes (60-XX) 3 Algebraic geometry (14-XX) 3 Approximations and expansions (41-XX) 2 General and overarching topics; collections (00-XX) 2 Commutative algebra (13-XX) 2 Real functions (26-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral transforms, operational calculus (44-XX) 2 Geophysics (86-XX) 1 Field theory and polynomials (12-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year