A generalized dressing approach for solving the extended KP and the extended mKP hierarchy

DOI10.1063/1.3126494zbMath1187.35218arXiv0905.1402OpenAlexW2015932819MaRDI QIDQ3565274

No author found.

Publication date: 3 June 2010

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

Full work available at URL: https://arxiv.org/abs/0905.1402

zbMATH Keywords

solitonseigenvalues and eigenfunctionsKorteweg--de Vries equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Related Items (13)

Links between \((\gamma_n, \sigma_k)\)-KP hierarchy, \((\gamma_n, \sigma_k)\)-mKP hierarchy, and \((2+1)-(\gamma_n, \sigma_k)\)-Harry Dym hierarchy ⋮ A new extended matrix KP hierarchy and its solutions ⋮ Cauchy matrix approach to integrable equations with self-consistent sources and the Yajima-Oikawa system ⋮ Virasoro symmetries of the constrained dispersionless mKP hierarchy ⋮ Generalized Darboux transformation for the discrete Kadomtsev-Petviashvili equation with self-consistent sources ⋮ A new bidirectional generalization of (2+1)-dimensional matrix k-constrained Kadomtsev-Petviashvili hierarchy ⋮ Discrete KP equation with self-consistent sources ⋮ Generalized dressing method for the extended two-dimensional Toda lattice hierarchy and its reductions ⋮ Commutativity of the extended KP flows ⋮ Bilinear Identities and Hirota's Bilinear Forms for an Extended Kadomtsev-Petviashvili Hierarchy ⋮ Extended KdV equations generated by squared eigenfunction symmetry ⋮ An extended noncommutative KP hierarchy ⋮ Additional reductions in the \(k\)-constrained modified KP hierarchy

Cites Work

• A new extended KP hierarchy
• On equations for wave interactions
• Solitons and infinite dimensional Lie algebras
• Transformation groups for soliton equations. Euclidean Lie algebras and reduction of the KP hierarchy
• Multi-scale expansions in the theory of systems integrable by the inverse scattering transform
• A direct method for deriving a multi-soliton solution for the problem of interaction of waves on the x,y plane
• Constrained KP hierarchy and bi-Hamiltonian structures
• Darboux theorems and Wronskian formulas for integrable systems. I: Constrained KP flows
• A new dual symmetry structure of the KP hierarchy.
• Bäcklund transformations for the KP and mKP hierarchies with self-consistent sources
• A new extended q-deformed KP hierarchy
• Two New Multi-component BKP Hierarchies
• Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–
• Constraints of the Kadomtsev–Petviashvili hierarchy
• Schlesinger–Bäcklund transformations for the N-component KP
• The n-component KP hierarchy and representation theory
• Wronskian solutions of the constrained Kadomtsev–Petviashvili hierarchy
• An extended two-dimensional Toda lattice hierarchy and two-dimensional Toda lattice with self-consistent sources
• A new multicomponent CKP hierarchy and solutions

This page was built for publication: A generalized dressing approach for solving the extended KP and the extended mKP hierarchy