Hermite–Padé approximations with Pfaffian structures: Novikov peakon equation and integrable lattices

Motivated by the Novikov equation and its peakon problem, we propose a new mixed type Hermite–Padé approximation whose unique solution is sequence of polynomials constructed with help Pfaffians. These belong to family recently proposed partial-skew-orthogonal polynomials. The relevance especially visible in problem germane so that obtain explicit inverse formulae terms Pfaffians reformulating spectral for multipeakons. Furthermore, investigate two approximations related discrete dual cubic string, show these problems can also be solved nonsymmetric Cauchy biorthogonal This formulation results correspondence among several integrable lattices.