Bihamiltonian Systems of Hydrodynamic Type and Reciprocal Transformations

Deformations of Semisimple Bihamiltonian Structures of Hydrodynamic Type

We classify in this paper infinitesimal quasitrivial deformations of semisimple bihamiltonian structures of hydrodynamic type.

On the Quasitriviality of Deformations of Bihamiltonian Structures of Hydrodynamic Type

We prove in this paper the quasitriviality of a class of deformations of the one component bihamiltonian structures of hydrodynamic type.

Deformations of bihamiltonian structures of hydrodynamic type

In this paper we study the deformations of bihamiltonian PDEs of hydrodynamic type with one dependent variable. The reason we study such deformations is that the deformed systems maintain an infinite number of commuting integrals of motion up to a certain order in the deformation parameter. This fact suggests that these systems could have, at least for small times, multi-solitons solutions. Our numerical experiments confirm this hypothesis.

On the moduli space of deformations of bihamiltonian hierarchies of hydrodynamic type

We investigate the deformation theory of the simplest bihamiltonian structure of hydrodynamic type, that of the dispersionless KdV hierarchy. We prove that all of its deformations are quasi-trivial in the sense of B. Dubrovin and Y. Zhang, that is, trivial after allowing transformations where the first partial derivative of the field is inverted. We reformulate the question about deformations as a question about the cohomology of a certain double complex, and calculate the appropriate cohomology group.

Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed

We prove that the bihamiltonian cohomology of a semisimple pencil of Poisson brackets of hydrodynamic type vanishes for almost all degrees. This implies the existence of a full dispersive deformation of a semisimple bihamiltonian structure of hydrodynamic type starting from any infinitesimal deformation.

2D-Toda层级的非对称有理约化与一类广义Frobenius流形

Asymmetric rational reductions of 2D-Toda hierarchy and a generalized Frobenius manifold

该研究分析了两类非对称2D-Toda层级有理约化的局部双哈密顿结构，构造了对应(2,1)型的三维广义Frobenius流形，并建立了其与双分次Toda、约束KP层级的变换关联。