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NONLINEAR EQUATIONS WITH INTEGRATED OPERATOR STRUCTURES
Вестник Северо-Кавказского федерального университета, 2022 The article is devoted to the construction of nonlinear equations with partial derivatives possessing Lax operator structure. The presence of Lax pair is supposed to allow to integrate the obtained equations with the help of the inverse scattering ...
Valentina M. Karslieva
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Lax Pair for a Novel Two-Dimensional Lattice [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 In paper by I.T. Habibullin and our joint paper the algorithm for classification of integrable equations with three independent variables was proposed. This method is based on the requirement of the existence of an infinite set of Darboux integrable reductions and on the notion of the characteristic Lie-Rinehart algebras. The method was applied for the
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Calogero-Moser Models III: Elliptic Potentials and Twisting
, 1998 Universal Lax pairs of the root type with spectral parameter and independent coupling constants for twisted non-simply laced Calogero-Moser models are constructed.
Bordner, A. J., Sasaki, R.
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A Note on Lax Pairs of the Sawada-Kotera Equation
Journal of Mathematics, 2014 We prove that the new Lax pair of the Sawada-Kotera equation, discovered recently by Hickman, Hereman, Larue, and Göktaş, and the well-known old Lax pair of this equation, considered in the form of zero-curvature representations, are gauge equivalent to ...
Sergei Sakovich
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St\"ackel transform of Lax equations
, 2019 We construct Lax pairs for a wide class of St\"ackel systems by applying the multi-parameter St\"ackel transform to Lax pairs of a suitably chosen systems from the seed class.
Blaszak, Maciej, Marciniak, Krzysztof
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Lax Pairs for the Discrete Reduced Nahm Systems [PDF]
Mathematical Physics, Analysis and Geometry, 2021 We discretise the Lax pair for the reduced Nahm systems and prove its equivalence with the Kahan-Hirota-Kimura discretisation procedure. We show that these Lax pairs guarantee the integrability of the discrete reduced Nahm systems providing an invariant.
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A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms
Symmetry, Integrability and Geometry: Methods and Applications, 2011 We expand the completeness study instigated in [J. Math. Phys. 50 (2009), 103516, 29 pages] which found all 2×2 Lax pairs with non-zero, separable terms in each entry of each Lax matrix, along with the most general nonlinear systems that can be ...
Mike C. Hay
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Two-Component Super AKNS Equations and Their Finite-Dimensional Integrable Super Hamiltonian System
Abstract and Applied Analysis, 2014 Starting from a matrix Lie superalgebra, two-component super AKNS system is constructed. By making use of monononlinearization technique of Lax pairs, we find that the obtained two-component super AKNS system is a finite-dimensional integrable super ...
Jing Yu, Jingwei Han
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Lax pair for strings in Lunin-Maldacena background [PDF]
Journal of High Energy Physics, 2005 Recently Lunin and Maldacena used an SL(3,R) transformation of the AdS_5 x S^5 background to generate a supergravity solution dual to a so-called beta-deformation of N = 4 super Yang-Mills theory. We use a T-duality-shift-T-duality (TsT) transformation to obtain the beta-deformed background for real beta, and show that solutions of string theory ...
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Explicit solutions of rational integrable differential-difference equations
Partial Differential Equations in Applied Mathematics, 2022 The rational integrable differential-difference equations are proposed from a different discrete spectral problem. We proved the Liouville integrability of rational integrable differential-difference equations by deriving its bi-Hamiltonian structures ...
Qiulan Zhao, Muhammad Arham Amin
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