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