Matches in SemOpenAlex for { <https://semopenalex.org/work/W242523008> ?p ?o ?g. }
Showing items 1 to 89 of
89
with 100 items per page.
- W242523008 abstract "For integrable systems in the sense of multidimensional consistency (MDC) we can consider the Lagrangian as a form, which is closed on solutions of the equations of motion. For 2-dimensional systems, described by partial difference equations with two independent variables, MDC allows us to define an action on arbitrary 2-dimensional surfaces embedded in a higher dimensional space of independent variables, where the action is not only a functional of the field variables but also the choice of surface. It is then natural to propose that the system should be derived from a variational principle which includes not only variations with respect to the dependent variables, but also with respect to variations of the surface in the space of independent variables. Here we derive the resulting system of generalized Euler-Lagrange equations arising from that principle. We treat the case where the equations are 2 dimensional (but which due to MDC can be consistently embedded in higher-dimensional space), and show that they can be integrated to yield relations of quadrilateral type. We also derive the extended set of Euler-Lagrange equations for 3-dimensional systems, i.e., those for equations with 3 independent variables. The emerging point of view from this study is that the variational principle can be considered as the set of equations not only encoding the equations of motion but as the defining equations for the Lagrangians themselves." @default.
- W242523008 created "2016-06-24" @default.
- W242523008 creator A5008767800 @default.
- W242523008 creator A5035447074 @default.
- W242523008 date "2018-05-03" @default.
- W242523008 modified "2023-09-27" @default.
- W242523008 title "A Variational Principle for Discrete Integrable Systems" @default.
- W242523008 cites W1493386851 @default.
- W242523008 cites W1501848164 @default.
- W242523008 cites W1976778088 @default.
- W242523008 cites W1998544592 @default.
- W242523008 cites W2009020885 @default.
- W242523008 cites W2015844927 @default.
- W242523008 cites W2023242456 @default.
- W242523008 cites W2093187073 @default.
- W242523008 cites W2095241583 @default.
- W242523008 cites W2118065183 @default.
- W242523008 cites W2290513778 @default.
- W242523008 cites W2507743553 @default.
- W242523008 cites W2962961287 @default.
- W242523008 cites W3100876231 @default.
- W242523008 cites W3102822779 @default.
- W242523008 cites W3102872111 @default.
- W242523008 cites W3105369713 @default.
- W242523008 cites W3106275102 @default.
- W242523008 doi "https://doi.org/10.3842/sigma.2018.041" @default.
- W242523008 hasPublicationYear "2018" @default.
- W242523008 type Work @default.
- W242523008 sameAs 242523008 @default.
- W242523008 citedByCount "1" @default.
- W242523008 countsByYear W2425230082017 @default.
- W242523008 crossrefType "journal-article" @default.
- W242523008 hasAuthorship W242523008A5008767800 @default.
- W242523008 hasAuthorship W242523008A5035447074 @default.
- W242523008 hasBestOaLocation W2425230081 @default.
- W242523008 hasConcept C121332964 @default.
- W242523008 hasConcept C134306372 @default.
- W242523008 hasConcept C14037181 @default.
- W242523008 hasConcept C170036204 @default.
- W242523008 hasConcept C200602138 @default.
- W242523008 hasConcept C200741047 @default.
- W242523008 hasConcept C2780791683 @default.
- W242523008 hasConcept C28826006 @default.
- W242523008 hasConcept C33923547 @default.
- W242523008 hasConcept C38409319 @default.
- W242523008 hasConcept C62520636 @default.
- W242523008 hasConcept C74650414 @default.
- W242523008 hasConcept C78045399 @default.
- W242523008 hasConcept C9259290 @default.
- W242523008 hasConcept C93779851 @default.
- W242523008 hasConcept C94523830 @default.
- W242523008 hasConcept C97985569 @default.
- W242523008 hasConceptScore W242523008C121332964 @default.
- W242523008 hasConceptScore W242523008C134306372 @default.
- W242523008 hasConceptScore W242523008C14037181 @default.
- W242523008 hasConceptScore W242523008C170036204 @default.
- W242523008 hasConceptScore W242523008C200602138 @default.
- W242523008 hasConceptScore W242523008C200741047 @default.
- W242523008 hasConceptScore W242523008C2780791683 @default.
- W242523008 hasConceptScore W242523008C28826006 @default.
- W242523008 hasConceptScore W242523008C33923547 @default.
- W242523008 hasConceptScore W242523008C38409319 @default.
- W242523008 hasConceptScore W242523008C62520636 @default.
- W242523008 hasConceptScore W242523008C74650414 @default.
- W242523008 hasConceptScore W242523008C78045399 @default.
- W242523008 hasConceptScore W242523008C9259290 @default.
- W242523008 hasConceptScore W242523008C93779851 @default.
- W242523008 hasConceptScore W242523008C94523830 @default.
- W242523008 hasConceptScore W242523008C97985569 @default.
- W242523008 hasLocation W2425230081 @default.
- W242523008 hasLocation W2425230082 @default.
- W242523008 hasLocation W2425230083 @default.
- W242523008 hasLocation W2425230084 @default.
- W242523008 hasOpenAccess W242523008 @default.
- W242523008 hasPrimaryLocation W2425230081 @default.
- W242523008 hasRelatedWork W1520787580 @default.
- W242523008 hasRelatedWork W1656407315 @default.
- W242523008 hasRelatedWork W1982123151 @default.
- W242523008 hasRelatedWork W2034478463 @default.
- W242523008 hasRelatedWork W2074883048 @default.
- W242523008 hasRelatedWork W242523008 @default.
- W242523008 hasRelatedWork W2800489564 @default.
- W242523008 hasRelatedWork W3123882228 @default.
- W242523008 hasRelatedWork W3205179556 @default.
- W242523008 hasRelatedWork W4378469897 @default.
- W242523008 isParatext "false" @default.
- W242523008 isRetracted "false" @default.
- W242523008 magId "242523008" @default.
- W242523008 workType "article" @default.