Dispersionless Hirota Equations of Two-Component BKP Hierarchy

The BKP hierarchy has a two-component analogue (the 2-BKP hierarchy). Dispersionless limit of this multi-component hierarchy is considered on the level of the $\tau$-function. The so called dispersionless Hirota equations are obtained from the Hirota equations of the $\tau$-function. These dispersionless Hirota equations turn out to be equivalent to a system of Hamilton–Jacobi equations. Other relevant equations, in particular, dispersionless Lax equations, can be derived from these fundamental equations. For comparison, another approach based on auxiliary linear equations is also presented.