Bilinear equations in Darboux transformations by boson-fermion correspondence

DOI10.1016/j.physd.2022.133198zbMath1486.81178arXiv2101.02520OpenAlexW3119780388MaRDI QIDQ2670259

Jipeng Cheng, Yi Yang

Publication date: 10 March 2022

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.02520

zbMATH Keywords

Darboux transformationsboson-fermion correspondencetau functionsbilinear equationssquared eigenfunction potential

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Groups and algebras in quantum theory and relations with integrable systems (81R12) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Euler-Poisson-Darboux equations (35Q05) Special quantum systems, such as solvable systems (81Q80) Particle exchange symmetries in quantum theory (general) (81V72)

Related Items (9)

Modified DKP hierarchy as modified BKP hierarchy ⋮ Super modified KP hierarchy in Kac–van de Leur construction ⋮ Several integrable properties of the discrete KP hierarchy obtained by means of gauge transformations ⋮ Darboux transformations of the modified BKP hierarchy by fermionic approach ⋮ Symmetries and bilinear equations for the modified BKP hierarchy ⋮ Solutions of the universal character hierarchy and BUC hierarchy by fermionic approach ⋮ Two types of universal characters and the integrable hierarchies ⋮ CKP hierarchy and free bosons ⋮ Nonlocal integrable equations from the mKP hierarchy

Cites Work

• Gromov-Witten theory of Fano orbifold curves, gamma integral structures and ADE-Toda hierarchies
• Solving bi-directional soliton equations in the KP hierarchy by gauge transformation
• Solitons and infinite dimensional Lie algebras
• The extended D-Toda hierarchy
• Pfaffian and determinantal tau functions
• On the BKP hierarchy: Additional symmetries, Fay identity and Adler-Shiota-Van Moerbeke formula
• Solving the KP hierarchy by gauge transformations
• Method of squared eigenfunction potentials in integrable hierarchies of KP type
• Vertex operator solutions to the discrete KP-hierarchy
• Modified KP and discrete KP
• Darboux theorems and Wronskian formulas for integrable systems. I: Constrained KP flows
• On additional symmetries of the KP hierarchy and Sato's Bäcklund transformation
• Squared eigenfunction symmetries for soliton equations. I
• Geometric Bäcklund-Darboux transformations for the KP hierarchy
• On the modified KP hierarchy: tau functions, squared eigenfunction symmetries and additional symmetries
• Lump solutions to nonlinear partial differential equations via Hirota bilinear forms
• BKP hierarchy and Pfaffian point process
• Open intersection numbers, matrix models and MKP hierarchy
• Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions
• The determinant representation of the gauge transformation operators
• A Lax representation for the vertex operator and the central extension
• Free fermions and tau-functions
• Hirota quadratic equations for the extended Toda hierarchy
• Coupled modified KP hierarchy and its dispersionless limit
• Mathematics of dispersive water waves
• Darboux Transformations for the KP Hierarchy in the Segal-Wilson Setting
• A Remark on the Commuting Flows Defined by Lax Equations
• Hirota equations for the extended bigraded Toda hierarchy and the total descendent potential of $\mathbb {C}P^1$ orbifolds
• Gauge transformations for the constrained CKP and BKP hierarchies
• Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–
• The fermionic approach to Darboux transformations
• GAUGE TRANSFORMATIONS AND RECIPROCAL LINKS IN 2 + 1 DIMENSIONS
• Bilinear equations for the constrained KP hierarchy
• Bilinear form and solutions of the k -constrained Kadomtsev - Petviashvili hierarchy
• Miura and auto-Bäcklund transformations for the cKP and cmKP hierarchies
• Introduction to Classical Integrable Systems
• General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions
• Symmetry reductions of the BKP hierarchy
• Sato–Bäcklund transformations and string equations of the mKP hierarchy
• Bilinear identities for the constrained modified KP hierarchy
• Polynomial tau-functions of BKP and DKP hierarchies
• The gauge transformation of the modified KP hierarchy
• The “ghost” symmetry of the BKP hierarchy
• On the constrained B-type Kadomtsev–Petviashvili hierarchy: Hirota bilinear equations and Virasoro symmetry
• Supersymmetric BKP systems and their symmetries
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Bilinear equations in Darboux transformations by boson-fermion correspondence