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Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We express AKNS hierarchies, admitting reductions to matrix NLS and matrix mKdV hierarchies, in terms of a bidifferential graded algebra. Application of a universal result in this framework quickly generates an infinite family of exact solutions ...
Aristophanes Dimakis +1 more
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Miura and Darboux transformations in the SUSY KP hierarchies
Nuclear Physics B, 2022 The Miura links between the KP and modified KP hierarchies are extended to the SUSY KP (SKP) and SUSY modified KP hierarchies (SmKP) of Manin Radul and Jacobian types.
Huizhan Chen, Jipeng Cheng, Zhiwei Wu
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q-deformation of corner vertex operator algebras by Miura transformation
Journal of High Energy Physics, 2021 Recently, Gaiotto and Rapcak proposed a generalization of W N algebra by considering the symmetry at the corner of the brane intersection (corner vertex operator algebra).
Koichi Harada +3 more
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Negative flows of generalized KdV and mKdV hierarchies and their gauge-Miura transformations
Journal of High Energy Physics, 2023 The KdV hierarchy is a paradigmatic example of the rich mathematical structure underlying integrable systems and has far-reaching connections in several areas of theoretical physics.
Ysla F. Adans +4 more
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Inverse spectral problem for Jacobi operators and Miura transformation
Concrete Operators, 2021 We study a Miura-type transformation between Kac - van Moerbeke (Volterra) and Toda lattices in terms of the inverse spectral problem for Jacobi operators, which appear in the Lax representation for such systems.
Osipov Andrey
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Abstract Formulation of the Miura Transform
Mathematics, 2020 Miura transform is known as the transformation between Korweg de-Vries equation and modified Korweg de-Vries equation. Its formal similarity to the Cole-Hopf transform has been noticed.
Yoritaka Iwata
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Comments on the negative grade KdV hierarchy
SciPost Physics Proceedings, 2023 The construction of negative grade KdV hierarchy is proposed in terms of a Miura-gauge transformation. Such gauge transformation is employed within the zero curvature representation and maps the Lax operator of the mKdV into its couterpart within the KdV
Y. F. Adans, Jose F. Gomes, G. V. Lobo, A. H. Zimerman
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Deficiency indices of block Jacobi matrices and Miura transformation
Special Matrices, 2022 We study the infinite Jacobi block matrices under the discrete Miura-type transformations which relate matrix Volterra and Toda lattice systems to each other and the situations when the deficiency indices of the corresponding operators are the same.
Osipov Andrey
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Miura-Reciprocal Transformation and Symmetries for the Spectral Problems of KdV and mKdV
Mathematics, 2021 We present reciprocal transformations for the spectral problems of Korteveg de Vries (KdV) and modified Korteveg de Vries (mKdV) equations. The resulting equations, RKdV (reciprocal KdV) and RmKdV (reciprocal mKdV), are connected through a transformation
Paz Albares, Pilar Garcia Estévez
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Miura-Type Transformations for Integrable Lattices in 3D
Mathematics, 2023 This article studies a class of integrable semi-discrete equations with one continuous and two discrete independent variables. At present, in the literature there are nine integrable equations of the form un+1,xj=f(un,xj,unj+1,unj,un+1j,un+1j−1) up to ...
Ismagil T. Habibullin +2 more
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