Symbolic computation of Lax pairs of partial difference equations using consistency around the cube
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Publication:372869
DOI10.1007/s10208-012-9133-9zbMath1306.37067arXiv1308.5473OpenAlexW2133041045MaRDI QIDQ372869
T. Bridgman, Peter H. van der Kamp, Willy Hereman, Gilles Reinout Willem Quispel
Publication date: 21 October 2013
Published in: Foundations of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1308.5473
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Additive difference equations (39A10)
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Cites Work
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- On solving large systems of polynomial equations appearing in discrete differential geometry
- Classification of three-dimensional integrable scalar discrete equations
- A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
- Lax pair for the Adler (lattice Krichever-Novikov) system
- Classification of integrable equations on quad-graphs. The consistency approach
- Symmetries and conservation laws of lattice Boussinesq equations
- The discrete and continuous Painlevé VI hierarchy and the Garnier systems
- A multidimensionally consistent version of Hirota’s discrete KdV equation
- Multi-Quadratic Quad Equations: Integrable Cases from a Factorized-Discriminant Hypothesis
- Boussinesq-like multi-component lattice equations and multi-dimensional consistency
- The staircase method: integrals for periodic reductions of integrable lattice equations
- Method for Solving the Korteweg-deVries Equation
- The lattice Gel'fand-Dikii hierarchy
- Prolongation structures of nonlinear evolution equations
- A Nonlinear Difference Scheme and Inverse Scattering
- On the Solution of a Class of Nonlinear Partial Difference Equations
- Direct Linearization of Extended Lattice BSQ Systems
- Duality for discrete integrable systems
- Integrals of nonlinear equations of evolution and solitary waves
- THE BOUSSINESQ INTEGRABLE SYSTEM: COMPATIBLE LATTICE AND CONTINUUM STRUCTURES
