Bilinear identities for an extended B-type Kadomtsev-Petviashvili hierarchy

TL;DR

This paper develops bilinear identities for an extended B-type KP hierarchy, enabling the derivation of Hirota's equations for related (2+1)-dimensional equations with self-consistent sources.

Contribution

It introduces a new extended BKP hierarchy framework with bilinear identities, linking wave functions, tau-functions, and Hirota's equations for complex integrable systems.

Findings

Constructed bilinear identities for the extended BKP hierarchy.

Derived Hirota's bilinear equations for two types of 2d-SKwS equations.

Provided explicit examples of Hirota's equations for these systems.

Abstract

In this paper, we construct the bilinear identities for the wave functions of an extended B-type Kadomtsev-Petviashvili (BKP) hierarchy, which contains two types of (2+1)-dimensional Sawada-Kotera equation with a self-consistent source (2d-SKwS-I and 2d-SKwS-II). By introducing an auxiliary variable corresponding to the extended flow for the BKP hierarchy, we find the tau-function and the bilinear identities for this extended BKP hierarchy. The bilinear identities can generate all the Hirota's bilinear equations for the zero-curvature forms of this extended BKP hierarchy. As examples, the Hirota's bilinear equations for the two types of 2d-SKwS (both 2d-SKwS-I and 2d-SKwS-II) will be given explicitly.