Miura and auto-Bäcklund transformations for the discrete KP and mKP hierarchies and their constrained cases

DOI10.1016/j.cnsns.2018.09.019OpenAlexW2894403928MaRDI QIDQ2206183

Jipeng Cheng, Jing-Song He

Publication date: 21 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2018.09.019

zbMATH Keywords

Miura transformationauto-Bäcklund transformationthe cdkp and cmdkp hierarchiesthe dkp and mdkp 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

Miura and Darboux transformations in the SUSY KP hierarchies, Several integrable properties of the discrete KP hierarchy obtained by means of gauge transformations, On the discrete modified KP hierarchies: the Wronskian solutions for their constrained cases, Constrained discrete KP hierarchy: the constraint on the tau functions and gauge transformations, Bäcklund transformation, exact solutions and interaction behaviour of the (3+1)-dimensional Hirota-Satsuma-Ito-like equation, Solutions of the constrained mKP hierarchy by Boson-Fermion correspondence, Bäcklund transformations for nonlinear differential equations and systems

Cites Work

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• Ghost symmetry of the discrete KP hierarchy
• The determinant representation of the gauge transformation for the discrete KP hierarchy
• Gauge equivalence and \(l\)-reductions of the differential-difference KP equation
• Constrained KP hierarchy and bi-Hamiltonian structures
• Canonical property of the Miura maps between the MKP and KP hierarchies, continuous and discrete
• Lax pairs, symmetries and conservation laws of a differential-difference equation -- Sato's approach
• The Wronskian solution of the constrained discrete Kadomtsev-Petviashvili hierarchy
• Gauge transformations of constrained discrete modified KP systems with self-consistent sources
• Sato's Bäcklund transformations, additional symmetries and ASvM formula for the discrete KP hierarchy
• SYMMETRIES AND LIE ALGEBRA OF THE DIFFERENTIAL–DIFFERENCE KADOMSTEV–PETVIASHVILI HIERARCHY
• A new extended discrete KP hierarchy and a generalized dressing method
• GAUGE TRANSFORMATIONS AND RECIPROCAL LINKS IN 2 + 1 DIMENSIONS
• Miura and auto-Bäcklund transformations for the cKP and cmKP hierarchies
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
• The Virasoro action on the tau function for the constrained discrete KP hierarchy
• The compatibility of additional symmetry and gauge transformations for the constrained discrete Kadomtsev-Petviashvili hierarchy
• Miura and auto-Backlund transformations for the q-deformed KP and q-deformed modified KP hierarchies
• Virasoro type algebraic structure hidden in the constrained discrete Kadomtsev-Petviashvili hierarchy
• Integrability properties of the differential-difference Kadomtsev–Petviashvili hierarchy and continuum limits
• The string equation and the τ-function Witt constraints for the discrete Kadomtsev-Petviashvili hierarchy