A note on the dispersionless BKP hierarchy

On kernel formulas and dispersionless Hirota equations of the extended dispersionless BKP hierarchy

“…4 is an infinite-dimensional version of WDVV equations in which the number of variables t k is infinite. However, in [6], some finite-dimensional reductions of the EdBKP hierarchy have been obtained via Riemann-Hilbert construction. Therefore, it is quite natural to ask whether these solutions satisfy the finite-dimensional version of WDVV equations.…”

Dispersionless BKP Hierarchy and Quadrant Löwner Equation

“…If we define u(λ) by As is well known (cf., for example, [1]), a one-parameter family of conformal mappings from a slit domain to the upper half plane satisfies the chordal Löwner equation 4 . Hence the equation (3.2) is essentially an equation for conformal mappings from a slit domain to the quadrant (Fig.…”

Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries

“…the BKP hierarchy and CKP hierarchy. About the BKP hierarchy, a lot of studies on additional symmetries have been done, such as additional symmetries of the BKP hierarchy [33], dispersionless BKP hierarchy [31,34], twocomponent BKP hierarchy [24] and its reduced hierarchies [20,21], supersymmetric BKP hierarchy [25] and so on. Dispersionless integrable systems [26] are very important in the study of all kinds of nonlinear sciences in physics, particularly in the application on the topological field theory [27] and matrix models [28,29].…”