arXiv subjects

Zhaowen Yan

Publications and source records attributed to Zhaowen Yan.

6 recordsLinked to original sources

arXiv2026

Tau functions and correlation functions of the bosonic universal character hierarchy

This paper is concerned with the construction of the bosonic universal character (UC) hierarchy, whose tau functions are investigated within the framework of charged free bosons. The Lie algebra corresponding to the bosonic UC hierarchy is $\mathfrak{\widehat{gl}}_{2\infty}$. It is shown that the tau functions of bosonic UC hierarchy can be represented based on a series of ordered exponential operators. Furthermore, we derive correlation functions of the bosonic UC hierarchy, which can be expressed as the product of UCs. It is worth noting that the correlation functions of the bosonic UC hierarchy are the inverse of the correlation functions of the generalized phase model.

math-ph↗

arXiv2026

Generalized i-boson model and boxed BUC plane partitions

This paper is devoted to investigating the relation between the generalized i-boson model and boxed BUC plane partitions. The representation of the generalized i-boson algebra and the actions of the monodromy matrix operators on basis vectors have been studied. We also consider the actions of neutral fermion vertex operators on state vectors in terms of the neutral fermionic Fock space. With the help of the scalar product of the generalized i-boson model, the generating function for boxed BUC plane partitions is derived which can be represented as the products of Schur Q-functions. Moreover, the generating function for BUC plane partitions with the double scaling limit is presented.

math-ph↗

arXiv2026

Boxed UC plane partitions and the two-site generalized phase model

This study investigates the connection between boxed UC plane partitions and the two-site generalized phase model. By introducing two maps, we investigate the representation of two-side generalized phase algebras and actions of monodromy matrix operators on basis vectors. The generating function of boxed UC plane partitions is established by the scalar product of the two-site generalized phase model, which can be expressed as products of Schur functions. It is shown that the generating function of boxed UC plane partitions is that of UC plane partitions with the double scaling limit.

math-ph↗

arXiv2022

Polynomial tau-functions of the symplectic KP, orthogonal KP and BUC hierarchies

This paper is concerned with the construction of the polynomial tau-functions of the symplectic KP (SKP), orthogonal KP (OKP) hierarchies and universal character hierarchy of B-type (BUC hierarchy), which are proved as zero modes of certain combinations of the generating functions. By applying the strategy of carrying out the action of the quantum fields on vacuum vector, the generating functions for symplectic Schur function, orthogonal Schur function and generalized Q-function have been presented. The remarkable feature is that polynomial tau-functions are the coefficients of certain family of generating functions. Furthermore, in terms of the Vandermonde-like identity and properties of Pfaffian, it is showed that the polynomial tau-functions of the SKP, OKP and BUC hierarchies canbe written as determinant and Pfaffian forms, respectively. In addition, the soliton solutions of the SKP and OKP hierarchies have been discussed.

nlin.SI↗

arXiv2020

Soliton molecules in Sharma-Tasso-Olver-Burgers equation

Soliton molecules have been experimentally discovered in optics and theoretically investigated for coupled systems. This paper is concerned with the formation of soliton molecules by the resonant mechanism for a noncoupled system, the Sharma-Tasso-Olver-Burgers (STOB) equation. In terms of introducing velocity resonance conditions, we derive the soliton (kink) molecules, half periodic kink (HPK) molecules and breathing soliton molecule of STOB equation. Meanwhile, the fission and fusion phenomena among kinks, kink molecules, HPKs and HPK molecules have been revealed. Moreover, we also discuss the central periodic kink solutions from the multiple solitary wave solutions.

nlin.PS↗

arXiv2019

Fifth-order generalized Heisenberg supermagnetic models

This paper is concerned with the construction of the fifth-order generalized Heisenberg supermagnetic models. We also investigate the integrable structure and properties of the supersymmetric systems. We establish their gauge equivalent equations with the gauge transformation for two quadratic constraints, i.e., the super fifth-order nonlinear Schrödinger equation and the fermionic fifth-order nonlinear Schrödinger equation, respectively.

nlin.SI↗