  The Novikov equation is an integrable analogue of the Camassa-Holm equation
with a cubic (rather than quadratic) nonlinear term. Both these equations
support a special family of weak solutions called multipeakon solutions. In
this paper, an approach involving Pfaffians is applied to study multipeakons of
the Novikov equation. First, we show that the Novikov peakon ODEs describe an
isospectral flow on the manifold cut out by certain Pfaffian identities. Then,
a link between the Novikov peakons and the finite Toda lattice of BKP type
(B-Toda lattice) is established based on the use of Pfaffians. Finally, certain
generalizations of the Novikov equation and the finite B-Toda lattice are
proposed together with special solutions. To our knowledge, it is the first
time that the peakon problem is interpreted in terms of Pfaffians.
