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Article
Mathematics, Applied
Denghui Li et al.
Summary: This paper focuses on the construction of the polynomial tau-functions (PTFs) for the orthogonal KP (OKP) hierarchy, multicomponent OKP hierarchy, and universal character hierarchy of B-type (BUC hierarchy). It is shown that the PTFs are zero modes of certain combinations of generating functions. The PTFs can be expressed as determinant and Pfaffian forms for the OKP and BUC hierarchies, respectively. The soliton solutions of the OKP hierarchy are also discussed.
JOURNAL OF GEOMETRY AND PHYSICS
(2023)
Article
Mathematics, Applied
Yi Yang et al.
Summary: This paper discusses the bilinear equations of the transformed tau functions under the successive applications of the Darboux transformations for the KP hierarchy, the modified KP hierarchy, and the BKP hierarchy. New bilinear equations are derived and examples are provided.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Physics, Mathematical
Denghui Li et al.
Summary: This paper presents the construction of quantum fields presentation and generating functions for orthogonal Schur functions and orthogonal universal characters (OUC). The boson-fermion correspondence for these two symmetric functions is discussed. Based on the quantum fields presentation, two integrable systems, namely orthogonal KP hierarchy (OKP) and OUC hierarchy, are obtained, with orthogonal Schur functions and orthogonal universal characters as their tau functions respectively. Furthermore, the (m, n)-soliton solution of the OUC hierarchy is discussed. Modified OKP and OUC hierarchies as extensions of integrable systems are also derived.
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
(2022)
Article
Physics, Mathematical
Wenchuang Guan et al.
Summary: In this paper, we investigate several topics related to the modified D-type Kadomtsev-Petviashvili (DKP) hierarchy. We first prove a conjecture that the product of the two tau functions in the modified DKP hierarchy is a tau function in the KP hierarchy. Then, we study the Darboux transformations of the DKP and modified DKP hierarchies. Finally, we provide solutions for the constrained BKP hierarchy in the fermionic representation of the infinite Lie algebra d(infinity).
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Chuanzhong Li
Summary: In this paper, the polynomial tau-function in terms of the universal characters of the universal character hierarchy is found, which can be treated as a zero mode of an appropriate combinatorial generating function. Furthermore, a multi-component UC hierarchy is defined and the polynomial tau-functions of the multi-component UC hierarchy are obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Physics, Mathematical
J. Harnad et al.
Summary: This paper presents a bilinear expansion for lattice elements of KP tau-functions labeled by partitions, showing a connection to BKP tau-functions labeled by strict partitions. The results extend previous findings on determinants and Pfaffians of skew symmetric matrices, with applications to Schur functions and Schur Q-functions. The expansion is derived using representations of KP and BKP tau-functions as vacuum expectation values of fermionic operators of charged and neutral type, respectively. The lattice structure is generated by charged creation and annihilation operators, and the result is obtained through factorization theorems for VEVs, with applications to inhomogeneous polynomial tau-functions.
JOURNAL OF MATHEMATICAL PHYSICS
(2021)
Article
Mathematics, Applied
J. Harnad et al.
Summary: An identity is derived that expresses Schur functions as sums over products of pairs of Schur Q-functions, generalizing known special cases. This identity is shown to follow from their representations as vacuum expectation values of products of charged or neutral fermionic creation and annihilation operators, Wick's theorem, and a factorization identity for VEVs of products of two mutually anticommuting sets of neutral fermionic operators.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Mathematics, Applied
Linjie Shi et al.
Summary: In this paper, an integrable system is constructed with solutions including orthogonal Schur functions and symplectic Schur functions. It is found that these functions can be obtained through a Boson-Fermion correspondence which differs slightly from the classical one. Additionally, a universal character satisfying the bilinear equation of a new infinite-dimensional integrable orthogonal UC hierarchy is constructed.
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
(2021)
Article
Mathematics, Applied
Huizhan Chen et al.
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
(2020)
Article
Physics, Mathematical
Fang Huang et al.
JOURNAL OF MATHEMATICAL PHYSICS
(2020)
Article
Physics, Particles & Fields
Na Wang et al.
EUROPEAN PHYSICAL JOURNAL C
(2019)
Article
Physics, Multidisciplinary
Yoko Shigyo
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2016)
Review
Mathematics, Applied
Alexander Alexandrov et al.
JOURNAL OF GEOMETRY AND PHYSICS
(2013)
Article
Mathematics
Teruhisa Tsuda
INTERNATIONAL JOURNAL OF MATHEMATICS
(2012)
Article
Mathematics, Applied
Metin Unal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2012)
Article
Mathematics, Applied
Metin Unal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2011)
Article
Mathematics, Applied
Metin Unal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2010)
Article
Mathematics
Yuji OGAWA
Tokyo Journal of Mathematics
(2010)
Article
Mathematics
T Tsuda
ADVANCES IN MATHEMATICS
(2005)
Article
Physics, Mathematical
T Tsuda
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2004)
