Integrable Systems. I

By Boris Dubrovin, I. Krichever, S. Novikov. 2001

424 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/84083a63ddc09a785374db5d3dcbd468a65cdfa7

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In Statistical and Nonlinear Physics

Citations in the corpus

Problem of time in quantum gravity (2010, methodology): “3 The Semiclassical Approach In the Semiclassical Approach [10, 42, 43, 4, 5, 46, 6, 13, 7], time is only meaningful in some semiclassical limit of the Quantum Gravity theory based on the WDE.”
On classical q-deformations of integrable σ-models (2013, methodology): “48) The compact real form Uq̂(f) of Uq̂(f ) then corresponds to the condition q̂ ∈ R and the following choice of ∗-involution on Uq̂(fC) [19] K̂ i = K̂i, Ê ∗ i = K̂ −1 i F̂i, F̂ ∗ i = ÊiK̂i.”
Special Lagrangian m-folds in ℂm with symmetries (2000, neutral): “An introduction to integrable systems is given in Hitchin, Segal and Ward [14].”
On the global well-posedness of the one-dimensional Schrodinger map flow (2008, positive): “Here we follow Chang, Shatah and Uhlenbeck [2000] and write the flow equation in terms of a parallel frame, with the added observation that the Kähler condition allows one to readily generalize their computations from the Riemann surface case to higher dimensions.”
Projective Transformations of Pseudo-Riemannian Manifolds (2003, background): “1) are the equations of the flow of the vector field ξH ([71,72,89,124].”
INTEGRABLE CLUSTER DYNAMICS OF DIRECTED NETWORKS AND PENTAGRAM MAPS (2014, neutral): “We are interested in the bracket associated with the trigonometric R-matrix (for the explicit formula for it, which we will not need, see [30]).”
Darboux Transformations in Integrable Systems: Theory and their Applications to Geometry (2005, background): “In [85], there are figures for some interesting surfaces including several surfaces of constant negative Gauss curvature.”
Quantum gravity: a progress report (2001, background): “[35] C. J. Isham, in Integrable systems, quantum groups, and quantum field theories , edited by L. A. Ibort and M. A. Rodŕıguez (Kluwer, Dordrecht, 1993).”
An overview of periodic elliptic operators (2015, background): “, those that lead to finitely many open gaps only, are very special and can be all described [112,113,306,307].”