Miura and auto-Backlund transformations for the q-deformed KP and q-deformed modified KP hierarchies

DOI10.1080/14029251.2016.1274111zbMath1420.35284OpenAlexW2564656085MaRDI QIDQ5231050

Jipeng Cheng

Publication date: 29 August 2019

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14029251.2016.1274111

zbMATH Keywords

Miura transformation\(q\)-KP and \(q\)-mKP hierarchiesauto-Backlund transformationconstrained \(q\)-KP and constrained \(q\)-mKP hierarchies

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Related Items (5)

Miura and Darboux transformations in the SUSY KP hierarchies ⋮ Several integrable properties of the discrete KP hierarchy obtained by means of gauge transformations ⋮ Solving the constrained modified KP hierarchy by gauge transformations ⋮ Miura and auto-Bäcklund transformations for the discrete KP and mKP hierarchies and their constrained cases ⋮ The gauge transformations of the constrained \(q\)-deformed modified KP hierarchy and their relations with the additional symmetries

Cites Work

• Unnamed Item
• Unnamed Item
• Sato theory on the \(q\)-Toda hierarchy and its extension
• Tau function solutions to a \(q\)-deformation of the KP hierarchy
• Constrained KP hierarchy and bi-Hamiltonian structures
• Canonical property of the Miura maps between the MKP and KP hierarchies, continuous and discrete
• On the \(q\)-deformed modified Korteweg-de Vries hierarchy
• On Darboux-Bäcklund transformations for the \(q\)-deformed Korteweg-de Vries hierarchy
• String equations of the \( q \)-KP hierarchy
• \(q\)-deformed KP hierarchy: Its additional symmetries and infinitesimal Bäcklund transformations
• The solution to the \(q\)-KdV equation
• Virasoro symmetry of constrained KP hierarchies
• Symmetric \(q\)-deformed KP hierarchy
• \(q\)-deformed KP hierarchy and \(q\)-deformed constrained KP hierarchy
• \(q\)-analogue of modified KP hierarchy and its quasi-classical limit
• Theq-deformed mKP hierarchy with self-consistent sources, Wronskian solutions and solitons
• A new extended q-deformed KP hierarchy
• Miura and auto-Bäcklund transformations for the cKP and cmKP hierarchies
• Theqdeformation of AKNS-D hierarchy
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
• The gauge transformation of the q-deformed modified KP hierarchy
• Quantum calculus

This page was built for publication: Miura and auto-Backlund transformations for the q-deformed KP and q-deformed modified KP hierarchies