The (n, 1)-Reduced DKP Hierarchy, the String Equation and W Constraints
نویسنده
چکیده
The total descendent potential of a simple singularity satisfies the Kac–Wakimoto principal hierarchy. Bakalov and Milanov showed recently that it is also a highest weight vector for the corresponding W -algebra. This was used by Liu, Yang and Zhang to prove its uniqueness. We construct this principal hierarchy of type D in a different way, viz. as a reduction of some DKP hierarchy. This gives a Lax type and a Grassmannian formulation of this hierarchy. We show in particular that the string equation induces a large part of the W constraints of Bakalov and Milanov. These constraints are not only given on the tau function, but also in terms of the Lax and Orlov–Schulman operators.
منابع مشابه
0 v 2 1 7 M ay 1 99 4 KDV TYPE HIERARCHIES , THE STRING EQUATION AND W 1 + ∞ CONSTRAINTS Johan
Abstract. To every partition n = n1 + n2 + · · · + ns one can associate a vertex operator realization of the Lie algebras a∞ and ĝln. Using this construction we make reductions of the s–component KP hierarchy, reductions which are related to these partitions. In this way we obtain matrix KdV type equations. Now assuming that (1) τ is a τ–function of the [n1, n2, . . . , ns]–th reduced KP hierar...
متن کاملAuxiliary linear problem , difference Fay identities and dispersionless limit of Pfaff - Toda hierarchy Kanehisa Takasaki
Recently the study of Fay-type identities revealed some new features of the DKP hierarchy (also known as “the coupled KP hierarchy” and “the Pfaff lattice”). Those results are now extended to a Toda version of the DKP hierarchy (tentatively called “the Pfaff-Toda hierarchy”) . Firstly, an auxiliary linear problem of this hierarchy is constructed. Unlike the case of the DKP hierarchy, building b...
متن کاملThe quasiclassical limit of the symmetry constraint of the KP hierarchy and the dispersionless KP hierarchy with self - consistent sources
For the first time we show that the quasiclassical limit of the symmetry constraint of the KP hierarchy leads to the generalized Zakharov reduction of the dispersionless KP (dKP) hierarchy which has been proved to be result of symmetry constraint of the dKP hierarchy recently. By either regarding the constrained dKP hierarchy as its stationary case or taking the dispersionless limit of the KP h...
متن کاملAuxiliary Linear Problem, Difference Fay Identities and Dispersionless Limit of Pfaff–Toda Hierarchy
Recently the study of Fay-type identities revealed some new features of the DKP hierarchy (also known as “the coupled KP hierarchy” and “the Pfaff lattice”). Those results are now extended to a Toda version of the DKP hierarchy (tentatively called “the Pfaff–Toda hierarchy”). Firstly, an auxiliary linear problem of this hierarchy is constructed. Unlike the case of the DKP hierarchy, building bl...
متن کاملShock formation in the dispersionless Kadomtsev-Petviashvili equation
The dispersionless Kadomtsev-Petviashvili (dKP) equation (ut + uux)x = uyy is one of the simplest nonlinear wave equations describing twodimensional shocks. To solve the dKP equation we use a coordinate transformation inspired by the method of characteristics for the one-dimensional Hopf equation ut + uux = 0. We show numerically that the solutions to the transformed equation develops singulari...
متن کامل