Two new multi-component BKP hierarchies

TL;DR

This paper introduces two novel multi-component BKP hierarchies derived from eigenfunction symmetry and nonstandard reductions, expanding the integrable systems framework with new equations and Lax representations.

Contribution

The paper proposes two new multi-component BKP hierarchies based on different reduction methods, including their Lax representations and reduction properties.

Findings

Both hierarchies admit reductions to k-constrained BKP and (1+1)-dimensional hierarchies.

The hierarchies include new SK equations with self-consistent sources.

Lax representations are explicitly constructed for the hierarchies.

Abstract

We firstly propose two kinds of new multi-component BKP (mcBKP) hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources which Lax representations are presented. The two mcBKP hierarchies both admit reductions to the $k-$constrained BKP hierarchy and to integrable (1+1)-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of bi-directional SK equations with self-consistent sources.