On a class of 2D integrable lattice equations
E. V. Ferapontov, I. T. Habibullin, M. N. Kuznetsova, V. S. Novikov
Abstract
We develop a new approach to the classification of integrable equations of the form uxy=f(u,ux,uy,△zu△z¯u,△zz¯u), where △z and △z¯ are the forward/backward discrete derivatives. The following two-step classification procedure is proposed: (1) First, we require that the dispersionless limit of the equation is integrable, that is, its characteristic variety defines a conformal structure, which is Einstein–Weyl, on every solution. (2) Second, to the candidate equations selected at the previous step, we apply the test of Darboux integrability of reductions obtained by imposing suitable cutoff conditions.
Topics & Concepts
Integrable systemMathematicsClass (philosophy)Lattice (music)Limit (mathematics)Conformal mapVariety (cybernetics)CutoffMathematical analysisMathematical physicsPure mathematicsDispersionless equationToda latticeLattice model (finance)PhysicsNonlinear Waves and SolitonsFractional Differential Equations SolutionsNumerical methods for differential equations