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

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

2010-11-09

arxiv.org/abs/1011.1978v1

J. Phys. A: Math. Theor. 44 (2011) 165204

Nonlinear Sciences

Exactly Solvable and Integrable Systems

24 pages

Scientific paper

10.1088/1751-8113/44/16/165204

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., $\tilde y z=\tilde x-x$. 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.

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