Boussinesq-like multi-component lattice equations and multi-dimensional consistency

2010/11/09 by Jarmo Hietarinta · 3 citations
Physics and Astronomy · #nlin.SI

paper · pdf · doi:10.1088/1751-8113/44/16/165204

published as J. Phys. A: Math. Theor. 44 (2011) 165204 · 24 pages

arxiv created 2010/11/09 · arxiv updated 2011/05/27

Abstract

We consider quasilinear, multi-variable, constant coefficient, lattice equations defined on the edges of the elementary square of the lattice, modeled after the lattice modified Boussinesq (lmBSQ) equation, e.g., y z= x-x. These equations are classified into three canonical forms and the consequences of their multidimensional consistency (Consistency-Around-the-Cube, CAC) are derived. One of the consequences is a restriction on form of the equation for the z variable, which in turn implies further consistency conditions, that are solved. As result we obtain a number of integrable multi-component lattice equations, some generalizing lmBSQ.

Cited by

• PGL(3)-invariant integrable systems from factorisation of linear differential and difference operators
• Discrete Gerdjikov-Ivanov models and their higher-order counterparts from the Cauchy matrix scheme
• On consistency around a 3 × 3× 3 cube and Q3 analogue of the lattice Boussinesq equation

Related

• On consistency around a 3 × 3× 3 cube and Q3 analogue of the lattice Boussinesq equation
• Search for CAC-integrable homogeneous quadratic triplets of quad equations and their classification by BT and Lax
• On non-multiaffine consistent-around-the-cube lattice equations
• A higher-rank version of the Q3 equation
• Consistency around a cube property of Hirota's discrete KdV equation and the lattice sine-Gordon equation