Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs

نویسندگان

  • Boris Dubrovin
  • Si-Qi Liu
  • Youjin Zhang
چکیده

Article history: Received 23 October 2014 Received in revised form 27 October 2015 Accepted 25 January 2016 Available online 24 February 2016 Communicated by Ravi Vakil MSC: primary 53D45 secondary 37K10

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Hodge Integrals and Integrable Hierarchies

We show that the generating series of some Hodge integrals involving one or two partitions are τ -functions of the KP hierarchy or the 2-Toda hierarchy respectively. We also formulate a conjecture on the connection between relative invariants and integrable hierarchies. The conjecture is verified in some examples.

متن کامل

Hamiltonian PDEs and Frobenius manifolds

In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the...

متن کامل

Hamiltonian perturbations of hyperbolic PDEs: from classification results to the properties of solutions

We begin with presentation of classification results in the theory of Hamiltonian PDEs with one spatial dimension depending on a small parameter. Special attention is paid to the deformation theory of integrable hierarchies, including an important subclass of the so-called integrable hierarchies of the topological type associated with semisimple Frobenius manifolds. Many well known equations of...

متن کامل

Integrable ODEs on Associative Algebras

In this paper we give definitions of basic concepts such as symmetries, first integrals, Hamilto-nian and recursion operators suitable for ordinary differential equations on associative algebras, and in particular for matrix differential equations. We choose existence of hierarchies of first integrals and/or symmetries as a criterion for integrability and justify it by examples. Using our compo...

متن کامل

A bi-Hamiltonian approach to the Sine-Gordon and Liouville hierarchies

where Pk(u, ux, ...) are differential polynomials. A central role in their approach is played by the bi-Hamiltonian structure of the dispersionless limit (ǫ = 0) of the hierarchy (1.1). Such structure consists of a pair of compatible local Poisson brackets of hydrodynamic type (see [4]). Very important examples of integrable PDEs such as the KdV equation, the continuous limit of the Toda lattic...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016