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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rational solutions of KP and BKP hierarchies through Toda lattice
户田晶格 KP BKP 层次结构 合理解
2023/4/27
The full Kostant-Toda lattice defined on simple Lie algebras can be viewed as finite version of KP type hierarchies. In this talk I will show you how to explicitly construct (all) rational solutions o...
KINETIC HIERARCHIES AND MACROSCOPIC LIMITS FOR CRYSTALLINE STEPS IN 1+1 DIMENSIONS
kinetic theory epitaxial growth crystal surface Burton–Cabrera–Frank model particle system Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy closure evaporation-condensation surface diffusion correlation function step chemical potential macroscopic limit propagation of chaos
2015/10/16
We apply methods of kinetic theory to study the passage from particle systems to nonlinear partial differential equations (PDEs) in the context of deterministic crystal surface relaxation. Starting wi...
The standardisation of mineral group hierarchies: application to recent nomenclature proposals
mineral group supergroup nomenclature mineral classification IMA朇NMNC
2013/12/6
A simplified definition of a mineral group is given on the basis of structural and compositional aspects. Then a hierarchical scheme for group nomenclature and mineral classification is introduced and...
Edge-based compartmental modeling for epidemic spread Part II: Model Selection and Hierarchies
epidemic spread Model Selection and Hierarchies Part II
2011/9/29
We consider the edge-based compartmental models for epidemic spread developed in [5]. We show conditions under which simpler models may be substituted for more detailed models, and in so doing we de n...
Exact Poisson pencils, $\tau$-structures and topological hierarchies
Dubrovin-Zhang’s perturbative integrable evolutionary PDEs
2011/7/5
We discuss, in the framework of Dubrovin-Zhang’s perturbative approach
to integrable evolutionary PDEs in 1+1 dimensions, the role of a special class
of Poisson pencils, called exact Poisson pencils...
Exact Poisson pencils, $T$-structures and topological hierarchies
$T$-structures topological hierarchies evolutionary PDEs
2011/7/27
Abstract: We discuss, in the framework of Dubrovin-Zhang's perturbative approach to integrable evolutionary PDEs in 1+1 dimensions, the role of a special class of Poisson pencils, called exact Poisson...
Hierarchies of Susy Splittings and Invisible Photinos as Dark Matter
Susy Splittings Invisible Photinos Dark Matter
2010/12/24
We explore how to generate hierarchies in the splittings between superpartners. Some of the consequences are the existence of invisible components of dark matter, new inflaton candidates, invisible mo...
The local well-posedness for Gross-Pitaevskii hierarchies
The local well-posedness Gross-Pitaevskii hierarchies
2010/11/24
We consider the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on $\mathbb{R}^n.$ By introducing a quasi-norm in certain Sobolev type spaces of sequences of marginal d...
Recursion operators for KP, mKP and Harry-Dym Hierarchies
Exactly Solvable and Integrable Systems(nlin.SI) Mathematical Physics(math-ph)
2010/11/10
In this paper, we give a unified construction of the recursion operators from the Lax representation for three integrable hierarchies: Kadomtsev-Petviashvili (KP), modified Kadomtsev-Petviashvili (mKP...
On rational solutions of multicomponent and matrix KP hierarchies
On rational solutions multicomponent matrix KP hierarchies
2010/11/10
We derive some rational solutions for the multicomponent and matrix KP hierarchies generalising an approach by Wilson. Connections with the multicomponent version of the KP/CM correspondence are discu...
Interpolating' differential reductions of multidimensional integrable hierarchies
differential reductions multidimensional integrable hierarchies
2010/11/10
We transfer the scheme of constructing differential reductions, developed recently for the case of the Manakov-Santini hierarchy, to the general multidimensional case. We consider in more detail the ...
The abelian hierarchy of quantum Hall states accounts for most of the states in the
lowest Landau level, and there is evidence of a similar hierarchy of non-abelian states
emanating from the ν = 5/2...
A polynomial bracket for the Dubrovin--Zhang hierarchies
polynomial bracket Dubrovin--Zhang hierarchies
2010/12/14
We define a hierarchy of Hamiltonian PDEs associ-ated to an arbitrary tau-function in the semi-simple orbit of the Givental group action on genus expansions of Frobenius manifolds.We prove that the eq...
Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation
Hodograph solutions scalar function Euler-Poisson-Darboux equation
2010/4/2
It is shown that the hodograph solutions of the dispersionless coupled KdV (dcKdV) hierarchies describe critical and degenerate critical points of a scalar function which obeys the Euler-Poisson-Darbo...
Canonical and grand canonical partition functions of Dyson gases as tau-functions of integrable hierarchies and their fermionic realization
partition functions integrable hierarchies Dyson gases
2010/4/2
The partition function for a canonical ensemble of 2D Coulomb charges in a background potential (the Dyson gas) is realized as a vacuum expectation value of a group-like element constructed in terms o...