Symbolic Computation of Lax Pairs of Partial Difference Equations using Consistency Around the Cube

• Published in: Foundations of computational mathematics Vol. 13; no. 4; pp. 517 - 544
• Main Authors: Bridgman, T., Hereman, W., Quispel, G. R. W., van der Kamp, P. H.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.08.2013; Springer; Springer Nature B.V
• Subjects: Applications of Mathematics; Computation; Computational mathematics; Computer Science; Cube; Cubes; Difference equations; Differential equations, Partial; Economics; Lattice theory; Lattices; Linear and Multilinear Algebras; Math Applications in Computer Science; Mathematical analysis; Mathematics; Mathematics and Statistics; Matrix Theory; Numerical Analysis; Partial differential equations; Quadrilaterals; Scalars; Schroedinger equation; Australia; Consistency around the cube; 82B20; 39A10; Lax pairs; 37K10; Integrable lattice equations

A three-step method due to Nijhoff and Bobenko & Suris to derive a Lax pair for scalar partial difference equations (PΔEs) is reviewed. The method assumes that the PΔEs are defined on a quadrilateral, and consistent around the cube. Next, the method is extended to systems of PΔEs where one has t...