This paper focuses on different reductions of the two-dimensional (2d)-Toda hierarchy.
Symmetric and skew-symmetric moment matrices are first considered, resulting in differential …

Bilinear equation is an important property for integrable nonlinear evolution equation. Many
famous research objects in mathematical physics, such as Gromov–Witten invariants, can be …

We consider systems of Brownian particles in the space of positive definite matrices, which
evolve independently apart from some simple interactions. We give examples of such …

We derive a formula for the connected n-point functions of a tau-function of the BKP
hierarchy in terms of its affine coordinates. This is a BKP-analogue of a formula for KP tau …

The solitons solution of BKP equation can be constructed by the Pfaffian structure. Then one
investigates the real line solitons structure of BKP equation using the totally non-negative …

The highest weight representation of the infinite Lie algebras is used to construct various
soliton equations by the famous Kyoto school. In this chapter, we firstly review the …

Starting with a skew-symmetric inner product over an elliptic curve, we propose the concept
of elliptic skew-orthogonal polynomials. Inspired by the Landau–Lifshitz hierarchy and its …

The modified BKP (mBKP) hierarchy is an important integrable hierarchy related with BKP
hierarchy. Darboux transformation is a powerful method to obtain various solutions of …

Abstract The modified Kadomtsev-Petviashvili hierarchy of B type (mBKP hierarchy) and its
constrained cases are investigated from the aspect of the Lax formulation. Starting from the …

The analogy between determinantal point processes (DPPs) and free fermionic calculi is
well-known. We point out that, from the perspective of free fermionic algebras, Pfaffian point …