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  1. Theoretical and Mathematical Physics
  2. Theoretical and Mathematical Physics : Volume 156
  3. Theoretical and Mathematical Physics : Volume 156, Issue 2, August 2008
  4. Darboux-integrable discrete systems
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Theoretical and Mathematical Physics : Volume 191
Theoretical and Mathematical Physics : Volume 190
Theoretical and Mathematical Physics : Volume 189
Theoretical and Mathematical Physics : Volume 188
Theoretical and Mathematical Physics : Volume 187
Theoretical and Mathematical Physics : Volume 186
Theoretical and Mathematical Physics : Volume 185
Theoretical and Mathematical Physics : Volume 184
Theoretical and Mathematical Physics : Volume 183
Theoretical and Mathematical Physics : Volume 182
Theoretical and Mathematical Physics : Volume 181
Theoretical and Mathematical Physics : Volume 180
Theoretical and Mathematical Physics : Volume 179
Theoretical and Mathematical Physics : Volume 178
Theoretical and Mathematical Physics : Volume 177
Theoretical and Mathematical Physics : Volume 176
Theoretical and Mathematical Physics : Volume 175
Theoretical and Mathematical Physics : Volume 174
Theoretical and Mathematical Physics : Volume 173
Theoretical and Mathematical Physics : Volume 172
Theoretical and Mathematical Physics : Volume 171
Theoretical and Mathematical Physics : Volume 170
Theoretical and Mathematical Physics : Volume 169
Theoretical and Mathematical Physics : Volume 168
Theoretical and Mathematical Physics : Volume 167
Theoretical and Mathematical Physics : Volume 166
Theoretical and Mathematical Physics : Volume 165
Theoretical and Mathematical Physics : Volume 164
Theoretical and Mathematical Physics : Volume 163
Theoretical and Mathematical Physics : Volume 162
Theoretical and Mathematical Physics : Volume 161
Theoretical and Mathematical Physics : Volume 160
Theoretical and Mathematical Physics : Volume 159
Theoretical and Mathematical Physics : Volume 158
Theoretical and Mathematical Physics : Volume 157
Theoretical and Mathematical Physics : Volume 156
Theoretical and Mathematical Physics : Volume 156, Issue 3, September 2008
Theoretical and Mathematical Physics : Volume 156, Issue 2, August 2008
Quadratic algebras related to elliptic curves
Differential equation for a functional integral
Integrable magnetic geodesic flows on lie groups
Darboux-integrable discrete systems
Problem of determining the nonstationary potential in a hyperbolic-type equation
Newtonian limit in the stabilized Randall-Sundrum model
Construction of invariant scalar particle wave equations on Riemannian manifolds with external gauge fields
Deformations of the central extension of the Poisson superalgebra
Verifying a new identity for Green’s functions of the n=1 supersymmetric non-Abelian Yang-Mills theory with matter fields
Radiation beyond four space-time dimensions
Description of weakly periodic Gibbs measures for the isingmodel on a cayley tree
Taking the particle interaction into account in a new concept of nucleation theory
Theoretical and Mathematical Physics : Volume 156, Issue 1, July 2008
Theoretical and Mathematical Physics : Volume 155
Theoretical and Mathematical Physics : Volume 154
Theoretical and Mathematical Physics : Volume 153
Theoretical and Mathematical Physics : Volume 152
Theoretical and Mathematical Physics : Volume 151
Theoretical and Mathematical Physics : Volume 150
Theoretical and Mathematical Physics : Volume 149
Theoretical and Mathematical Physics : Volume 148
Theoretical and Mathematical Physics : Volume 147
Theoretical and Mathematical Physics : Volume 146
Theoretical and Mathematical Physics : Volume 145
Theoretical and Mathematical Physics : Volume 144
Theoretical and Mathematical Physics : Volume 143
Theoretical and Mathematical Physics : Volume 142
Theoretical and Mathematical Physics : Volume 141
Theoretical and Mathematical Physics : Volume 140
Theoretical and Mathematical Physics : Volume 139
Theoretical and Mathematical Physics : Volume 138
Theoretical and Mathematical Physics : Volume 137
Theoretical and Mathematical Physics : Volume 136
Theoretical and Mathematical Physics : Volume 135
Theoretical and Mathematical Physics : Volume 134
Theoretical and Mathematical Physics : Volume 133
Theoretical and Mathematical Physics : Volume 132
Theoretical and Mathematical Physics : Volume 131
Theoretical and Mathematical Physics : Volume 130
Theoretical and Mathematical Physics : Volume 129
Theoretical and Mathematical Physics : Volume 128
Theoretical and Mathematical Physics : Volume 127
Theoretical and Mathematical Physics : Volume 126
Theoretical and Mathematical Physics : Volume 125
Theoretical and Mathematical Physics : Volume 124
Theoretical and Mathematical Physics : Volume 123
Theoretical and Mathematical Physics : Volume 122
Theoretical and Mathematical Physics : Volume 121
Theoretical and Mathematical Physics : Volume 120
Theoretical and Mathematical Physics : Volume 119
Theoretical and Mathematical Physics : Volume 118
Theoretical and Mathematical Physics : Volume 117
Theoretical and Mathematical Physics : Volume 116
Theoretical and Mathematical Physics : Volume 115
Theoretical and Mathematical Physics : Volume 114
Theoretical and Mathematical Physics : Volume 113
Theoretical and Mathematical Physics : Volume 112
Theoretical and Mathematical Physics : Volume 111
Theoretical and Mathematical Physics : Volume 110

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Darboux-integrable discrete systems

Content Provider Springer Nature Link
Author Vereshchagin, V. L.
Copyright Year 2008
Abstract We extend Laplace’s cascade method to systems of discrete “hyperbolic” equations of the form u$_{i+1,j+1 }$ = f(u$_{i+1,j}$, u$_{i,j+1 }$, u$_{i,j}$), where u$_{ij}$ is a member of a sequence of unknown vectors, i, j ∊ ℤ. We introduce the notion of a generalized Laplace invariant and the associated property of the system being “Liouville.” We prove several statements on the well-definedness of the generalized invariant and on its use in the search for solutions and integrals of the system. We give examples of discrete Liouville-type systems.
Starting Page 1142
Ending Page 1153
Page Count 12
File Format PDF
ISSN 00405779
Journal Theoretical and Mathematical Physics
Volume Number 156
Issue Number 2
e-ISSN 15739333
Language English
Publisher Springer US
Publisher Date 2008-08-30
Publisher Place Boston
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Laplace’s cascade method Darboux integrability nonlinear chain Applications of Mathematics Mathematical and Computational Physics
Content Type Text
Resource Type Article
Subject Statistical and Nonlinear Physics Mathematical Physics
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