Solving the KP hierarchy by gauge transformations
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Publication:1201395
DOI10.1007/BF02097625zbMath0756.35077OpenAlexW2015164084MaRDI QIDQ1201395
Publication date: 17 January 1993
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02097625
KdV equations (Korteweg-de Vries equations) (35Q53) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)
Related Items (38)
Modified DKP hierarchy as modified BKP hierarchy ⋮ Super modified KP hierarchy in Kac–van de Leur construction ⋮ A New Class of Soliton Solutions for the (Modified) Kadomtsev-Petviashvili Equation ⋮ Miura and Darboux transformations in the SUSY KP hierarchies ⋮ On UrKdV and UrKP ⋮ Darboux transformations for supersymmetric Korteweg-de Vries equations ⋮ Several integrable properties of the discrete KP hierarchy obtained by means of gauge transformations ⋮ Solving the constrained modified KP hierarchy by gauge transformations ⋮ Determinant representation of Darboux transformation for the AKNS system ⋮ Gauge transformations of two-component KP and mKP hierarchies ⋮ Bilinear equations in Darboux transformations by boson-fermion correspondence ⋮ Darboux transformations of the modified BKP hierarchy by fermionic approach ⋮ Constrained discrete KP hierarchy: the constraint on the tau functions and gauge transformations ⋮ Darboux transformations of new supersymmetric CKP and BKP hierarchies ⋮ The Wronskian solution of the constrained discrete Kadomtsev-Petviashvili hierarchy ⋮ Affine Lie algebraic origin of constrained KP hierarchies ⋮ Gauge transformations of constrained discrete modified KP systems with self-consistent sources ⋮ Solving bi-directional soliton equations in the KP hierarchy by gauge transformation ⋮ Solving the constrained KP hierarchy by gauge transformations ⋮ The Hopf-Cole transformation and the KP equation ⋮ The gauge transformations of the constrained \(q\)-deformed modified KP hierarchy and their relations with the additional symmetries ⋮ Gauge transformations for the constrained CKP and BKP hierarchies ⋮ Burgers and Kadomtsev-Petviashvili hierarchies: a functional representation approach ⋮ SOLITON RESONANCES FOR THE MODIFIED KADOMTSEV–PETVIASHVILI EQUATIONS IN UNIFORM AND NON-UNIFORM MEDIA ⋮ Miura and auto-Bäcklund transformations for the cKP and cmKP hierarchies ⋮ Two-peak soliton in the CKP hierarchy ⋮ The applications of the gauge transformation for the BKP hierarchy ⋮ Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions ⋮ The determinant representation of the gauge transformation for the discrete KP hierarchy ⋮ CKP hierarchy and free bosons ⋮ Binary Darboux–Bäcklund transformations for the Manin–Radul super KdV hierarchy ⋮ Supersymmetric Kadomtsev–Petviashvili hierarchy: “Ghost” symmetry structure, reductions, and Darboux–Bäcklund solutions ⋮ Gauge Transformation for BC r -KP Hierarchy and Its Compatibility with Additional Symmetry ⋮ Solutions of the (2 + 1)-Dimensional KP, SK and KK Equations Generated by Gauge Transformations from Nonzero Seeds ⋮ The gauge transformation of the q-deformed modified KP hierarchy ⋮ The compatibility of additional symmetry and gauge transformations for the constrained discrete Kadomtsev-Petviashvili hierarchy ⋮ The gauge transformation of the modified KP hierarchy ⋮ Geometric Bäcklund-Darboux transformations for the KP hierarchy
Cites Work
- Complete integrability of the Kadomtsev-Petviashvili equation
- Characterization of Jacobian varieties in terms of soliton equations
- On a class of polynomials connected with the Korteweg-de Vries equation
- Bäcklund transformations and their applications
- A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
- General determinants and the tau function for the Kadomtsev-Petviashvili hierarchy
- Landau-Lifshitz equation: solitons, quasi-periodic solutions and infinite-dimensional Lie algebras
- An alternative explicit construction of N-soliton solutions in 1+1 dimensions
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