KdV6: An integrable system

(KST)-S-2-T-2 [A. Karasu-Kalkani, A. Karasu, A. Sakovich, S. Sakovich, R. Turban, nlin/0708.3247] recently derived a new 6th-order wave equation KdV6: (partial derivative(2)(x) + 8u(x)partial derivative(x) + 4u(xx)) (u(t) + u(xxx) + 6u(x)(2)) = 0, found a linear problem and an auto-Backclund transformation for it, and conjectured its integrability in the usual sense. We prove this conjecture by constructing an infinite commuting hierarchy KdV(n)6 with a common infinite set of conserved densities. A general construction is presented applicable to any bi-Hamiltonian system (such as all standard Lax equations, continuous and discrete) providing a nonholonomic perturbation of it. This perturbation is conjectured to preserve integrability. That conjecture is verified in a few representative cases: the classical long-wave equations, the Toda lattice (both continuous and discrete), and the Euler top. (c) 2007 Elsevier B.V. All rights reserved.