Results 31 to 40 of about 2,243,156 (179)

Solutions for Several Quadratic Trinomial Difference Equations and Partial Differential Difference Equations in ${\mathbb{C}}^2$

Axioms, 2021
This article is to investigate the existence of entire solutions of several quadratic trinomial difference equations f(z+c)2+2αf(z)f(z+c)+f(z)2=eg(z), and the partial differential difference equations f(z+c)2+2αf(z+c)∂f(z)∂z1+∂f(z)∂z12=eg(z),f(z+c)2+2αf ...
Hong Li, Hongyan Xu
doaj   +1 more source

Differential Galois Theory of Linear Difference Equations [PDF]

, 2008
We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations.
Hardouin, Charlotte, Singer, Michael F.
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Galois theory of fuchsian q-difference equations [PDF]

, 2002
We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff's classification scheme with the connection matrix to define and describe their Galois groups.
Sauloy, Jacques
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Continuous Symmetries of Difference Equations

, 2005
Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations ...
Ablowitz M J, Ablowitz M J, Ablowitz M J, Ablowitz M J, Ablowitz M J, Aczel J, Aczel J, Adler V E, Ames W F, Anderson R L, Baĭkov V A, Baĭkov V A, Baĭkov V A, Bakirova M, Baumann G, Bluman G, Bluman G W, Bluman G W, Boiti M, Boutin M, Bruschi M, Bruschi M, Budd C, Byrnes G B, Calogero F, Cantwell B J, Cicogna G, Cicogna G, Decio Levi, DiBucchianico A, Dimakis A, Dodd R K, Dorodnitsyn V A, Dorodnitsyn V A, Dorodnitsyn V A, Dorodnitsyn V A, Durán A, Elaydi S, Faddeev L D, Fermi E Pasta J Ulam S, Fushchich V I, Fushchich V I, Fushchich W I, Gaeta G, Gaeta G, Gaeta G, Grammaticos B, Grammaticos B, Helgason S, Hereman W, Hernández Heredero R, Hernández Heredero R, Hernández Heredero R, Hernández Heredero R, Hernández Heredero R, Hietarinta J, Hietarinta J, Hill J M, Ibragimov N H, Ibragimov N H, Ibragimov N H, Ibragimov N H, Iserles A, Jacobson N, Jordan C, Kersten P H M, Kruskal M D, Lafortune S, Lamb J S W, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D, Levi D Gazeau J-P Kerner R Antoine J-P Métens S Thibon J-Y, Levi D Winternitz P Atakishiyev N M Seligman T H Wolf K B, Lie S, Lie S, Lie S, Lie S, Maeda S, Maeda S, Maeda S, Manakov S V, Martina L, Mikhailov A V, Milne-Thomson L M, Moody R V, Naimark M A, Newell A C, Niederer U, Nijhoff F Capel H W Hazewinkel M Capel H W de Jager E M, Nijhoff F W, Nijhoff F W, Nijhoff F W, Nijhoff F W, Nijhoff F W Papageorgiou V G Capel H W, Noether E, Novikov S, Olver P J, Ovsiannikov L V, Pavel Winternitz, Ramani A, Remoissenet M, Rodríguez M A, Rogers C, Roman S, Rota G C, Rota G C, Sahadevan R, Sahadevan R Byrnes G B Quispel G R W Levi D Vinet L Wintemitz P, Shabat A B, Sokolov V V, Steeb W-H, Stephani H, Stormark O, Suris, Tamizhmani K M, Thomas J W, Toda M, Toda M, Tzitzeica G, Tzitzeica G, Valiquette F, Winternitz P, Winternitz P, Winternitz P, Winternitz P, Winternitz P Corney S P Delbourgo R Jarvis P D, Winternitz P Levi D Winternitz P, Y-s Li, Zakharov V E   +154 more
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Reflectionless Potentials for Difference Schr\"odinger Equations [PDF]

, 2015
As a part of the program `discrete quantum mechanics,' we present general reflectionless potentials for difference Schr\"odinger equations with pure imaginary shifts. By combining contiguous integer wave number reflectionless potentials, we construct the
Odake, Satoru, Sasaki, Ryu
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Transformations of Difference Equations I

Advances in Difference Equations, 2010
We consider a general weighted second-order difference equation. Two transformations are studied which transform the given equation into another weighted second order difference equation of the same type, these are based on the Crum transformation.
Currie Sonja, Love AnneD
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Approximative solutions of difference equations

Electronic Journal of Qualitative Theory of Differential Equations, 2014
Asymptotic properties of solutions of difference equations of the form $$ \Delta^m x_n=a_nf(n,x_{\sigma(n)})+b_n $$ are studied. Using the iterated remainder operator and fixed point theorems we obtain sufficient conditions under which for any solution
Janusz Migda
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Quasi Exactly Solvable Difference Equations

, 2007
Several explicit examples of quasi exactly solvable `discrete' quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom.
Gendenshtein L. E., Ryu Sasaki
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A survey of Hirota's difference equations

, 1997
A review of selected topics in Hirota's bilinear difference equation (HBDE) is given. This famous 3-dimensional difference equation is known to provide a canonical integrable discretization for most important types of soliton equations.
A. Bobenko, A. Klümper, A. Kuniba, A. Orlov, A. Orlov, A. V. Zabrodin, A. Yu. Volkov, A. Zabrodin, Al. B. Zamolodchikov, B. A. Dubrovin, B. A. Dubrovin, D. Lebedev, E. Date, E. Date, E. Date, E. Date, F. Ravanini, G. Segal, I. M. Krichever, I. M. Krichever, K. Ueno, L. D. Faddeev, M. J. Martins, M. Jimbo, M. L. Kontsevich, M. Sato, R. Hirota, R. Hirota, R. Hirota, R. Hirota, R. Hirota, R. Hirota, R. Hirota, S. Kharchev, S. Kharchev, S. N. M. Ruijsenaars, S. Saito, T. Miwa, V. B. Matveev, V. B. Matveev, V. Spiridonov, Y. Ohta, Yu. Suris, Yu. Suris   +43 more
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Calculation of master integrals by difference equations [PDF]

, 2001
In this paper we describe a new method of calculation of master integrals based on the solution of systems of difference equations in one variable. An explicit example is given, and the generalization to arbitrary diagrams is described.
Laporta, S.
core   +3 more sources