Conformally Invariant Elliptic Liouville Equation and Its Symmetry-Preserving Discretization

[1]  P. Winternitz,et al.  Lie group classification of first-order delay ordinary differential equations , 2017, 1712.02581.

[2]  D. Bartolucci,et al.  Asymptotic blow-up analysis for singular Liouville type equations with applications , 2017 .

[3]  Alexander Bihlo,et al.  Symmetry-Preserving Numerical Schemes , 2016, 1608.02557.

[4]  D. Levi,et al.  On Partial Differential and Difference Equations with Symmetries Depending on Arbitrary Functions , 2015, 1512.01967.

[5]  Rutwig Campoamor-Stursberg,et al.  Symmetry preserving discretization of ordinary differential equations. Large symmetry groups and higher order equations , 2015, 1507.06428.

[6]  D. Levi,et al.  Structure preserving discretizations of the Liouville equation and their numerical tests , 2015, 1504.01953.

[7]  P. Winternitz,et al.  The adjoint equation method for constructing first integrals of difference equations , 2015 .

[8]  P. Winternitz,et al.  The Korteweg–de Vries equation and its symmetry-preserving discretization , 2014, 1409.4340.

[9]  D. Levi,et al.  Lie-point symmetries of the discrete Liouville equation , 2014, 1407.4043.

[10]  F. Valiquette,et al.  Invariant discretization of partial differential equations admitting infinite-dimensional symmetry groups , 2014, 1401.4380.

[11]  F. Valiquette,et al.  Symmetry preserving numerical schemes for partial differential equations and their numerical tests , 2011, 1110.5921.

[12]  P. Olver,et al.  Symmetry, Integrability and Geometry: Methods and Applications On the Structure of Lie Pseudo-Groups ⋆ , 2022 .

[13]  P. Winternitz,et al.  Invariant difference schemes and their application to invariant ordinary differential equations , 2009, 0906.2980.

[14]  Peter J. Olver,et al.  Moving Frames for Lie Pseudo–Groups , 2008, Canadian Journal of Mathematics.

[15]  G. Cicogna.  Symmetry classification of quasi-linear PDE’s containing arbitrary functions , 2007, math-ph/0702008.

[16]  G. Quispel,et al.  Geometric integrators for ODEs , 2006 .

[17]  P. Winternitz,et al.  Difference schemes with point symmetries and their numerical tests , 2006, math-ph/0602057.

[18]  P. Olver.  On Multivariate Interpolation , 2006 .

[19]  R. Jackiw.  Weyl symmetry and the Liouville theory , 2005, hep-th/0511065.

[20]  D. Levi,et al.  Continuous symmetries of difference equations , 2005, nlin/0502004.

[21]  Peter J. Olver,et al.  A Survey of Moving Frames , 2004, IWMM/GIAE.

[22]  Ron Buckmire,et al.  Application of a Mickens finite‐difference scheme to the cylindrical Bratu‐Gelfand problem , 2004 .

[23]  P. Winternitz,et al.  Lie symmetries and exact solutions of first-order difference schemes , 2004, nlin/0402047.

[24]  Y. Nakayama.  Liouville Field Theory — A decade after the revolution , 2004, hep-th/0402009.

[25]  P. Tempesta,et al.  Lorentz and Galilei Invariance on Lattices , 2003, hep-th/0310013.

[26]  P. Winternitz,et al.  Continuous symmetries of Lagrangians and exact solutions of discrete equations , 2003, nlin/0307042.

[27]  V. Dorodnitsyn,et al.  A Heat Transfer with a Source: the Complete Set of Invariant Difference Schemes , 2003, math/0309139.

[28]  A. Kiselev.  On the Geometry of Liouville Equation: Symmetries, Conservation Laws, and Bäcklund Transformations , 2002 .

[29]  Vladimir Dorodnitsyn,et al.  Noether-type theorems for difference equations , 2001 .

[30]  Chris Budd,et al.  Symmetry-adapted moving mesh schemes for the nonlinear Schrödinger equation , 2001 .

[31]  D. Levi,et al.  Lie symmetries of multidimensional difference equations , 2001, 0709.3238.

[32]  J. Marsden,et al.  Discrete mechanics and variational integrators , 2001, Acta Numerica.

[33]  J. Teschner.  Liouville theory revisited , 2001, hep-th/0104158.

[34]  D. Levi,et al.  Lie point symmetries of difference equations and lattices , 2000, 0709.3112.

[35]  V. E. Adler,et al.  Discrete analogues of the Liouville equation , 1999, solv-int/9902016.

[36]  V. Dorodnitsyn,et al.  Symmetry-preserving difference schemes for some heat transfer equations , 1997, math/0402367.

[37]  A. Orlov,et al.  Algebra of pseudodifferential operators and symmetries of equations in the Kadomtsev–Petviashvili hierarchy , 1997 .

[38]  A. Zamolodchikov,et al.  Conformal bootstrap in Liouville field theory , 1995 .

[39]  H. Dorn,et al.  On Correlation Functions for Non-critical Strings with c 1 , 1992, hep-th/9206053.

[40]  Pavel Winternitz,et al.  Group theoretical analysis of dispersive long wave equations in two space dimensions , 1990 .

[41]  Luigi Martina,et al.  Analysis and applications of the symmetry group of the multidimensional three-wave resonant interaction problem , 1989 .

[42]  D. Levi,et al.  Equations invariant under the symmetry group of the Kadomtsev-Petviashvili equation , 1988 .

[43]  Decio Levi,et al.  Symmetry reduction for the Kadomtsev–Petviashvili equation using a loop algebra , 1986 .

[44]  S. V. Talalov,et al.  Liouville field theory: IST and Poisson bracket structure , 1986 .

[45]  Levi,et al.  Subalgebras of loop algebras and symmetries of the Kadomtsev-Petviashvili equation. , 1985, Physical review letters.

[46]  W. I. Fushchich,et al.  The symmetry and some exact solutions of the nonlinear many-dimensional Liouville, d'Alembert and eikonal equations , 1983 .

[47]  A. Polyakov.  Quantum Geometry of Bosonic Strings , 1981 .

[48]  P. Medolaghi.  Sulla teoria dei gruppi infiniti continui , 1897 .

[49]  A. Its.  Symmetries and Integrability of Difference Equations: Discrete Painlevé Equations and Orthogonal Polynomials , 2011 .

[50]  A. Iserles.  A First Course in the Numerical Analysis of Differential Equations: Gaussian elimination for sparse linear equations , 2008 .

[51]  E. Hairer,et al.  Structure-Preserving Algorithms for Ordinary Differential Equations , 2006 .

[52]  Springer Berlin,et al.  Hongbo Li, Peter J. Olver, Gerald Sommer (eds.). Computer Algebra and Geometric Algebra with Applications , 2005 .

[53]  Roman Kozlov,et al.  Lie group classification of second-order ordinary difference equations , 2000 .

[54]  D. Crowdy.  General solutions to the 2D Liouville equation , 1997 .

[55]  Benoit Champagne,et al.  On the infinite‐dimensional symmetry group of the Davey–Stewartson equations , 1988 .

[56]  L. Takhtajan,et al.  Liouville model on the lattice , 1988 .

[57]  Alexander M. Polyakov,et al.  Gauge Fields And Strings , 1987 .