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Solving the two‐dimensional constant quantum Yang–Baxter equation
A detailed analysis of the constant quantum Yang–Baxter equation Rk1k2j1j2 Rl1k3k1j3Rl2l3k2k3= Rk2k3j2j3 Rk1l3j1k3Rl1l2k1k2 in two dimensions is presented, leading to an exhaustive list of its
A number of second order maps are presented, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable, and a more sensitive integrability test is proposed using the growth of the degree of its iterates.
Searching for CAC-maps
Abstract For two-dimensional lattice equations the standard definition of integrability is that it should be possible to extend the map consistently to three dimensions, i.e., that it is “consistent
Soliton solutions for ABS lattice equations: I. Cauchy matrix approach
In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable
A Search for Bilinear Equations Passing Hirota''s Three-Soliton Condition
In this paper the results of a search for complex bilinear equations with two‐soliton solutions are presented. The following basic types are discussed: (a) the nonlinear Schrodinger equation B(Dx,
Sasa-Satsuma higher-order nonlinear Schrödinger equation and its bilinearization and multisoliton solutions.
The correct bilinearization is given based on the interpretation of the Sasa-Satsuma equation as a reduction of the three-component Kadomtsev-Petviashvili hierarchy and multisoliton formulas are obtained.
Searching for integrable lattice maps using factorization
We analyse the factorization process for lattice maps, searching for integrable cases. The maps were assumed to be at most quadratic in the dependent variables, and we required minimal factorization
Discrete Systems and Integrability
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory