Results 21 to 30 of about 2,288,345 (293)
Acta Polytechnica, 2023 We generate solvable cases of the two angular equations resulting from variable separation in the three-dimensional Dunkl-Schrödinger equation expressed in spherical coordinates.
Axel Schulze-Halberg
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The multidimensional Darboux transformation [PDF]
Journal of Geometry and Physics, 1998 A generalization of the classical one-dimensional Darboux transformation to arbitrary n-dimensional oriented Riemannian manifolds is constructed using an intrinsic formulation based on the properties of twisted Hodge Laplacians. The classical two-dimensional Moutard transformation is also generalized to non-compact oriented Riemannian manifolds of ...
González López, Artemio, Kamran, Niky
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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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Yang–Baxter maps, Darboux transformations, and linear approximations of refactorisation problems [PDF]
Journal of Physics A: Mathematical and Theoretical, 2020 Yang–Baxter maps (YB maps) are set-theoretical solutions to the quantum Yang–Baxter equation. For a set X = Ω × V, where V is a vector space and Ω is regarded as a space of parameters, a linear parametric YB map is a YB map Y: X × X → X × X such that Y ...
V. Buchstaber +3 more
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Nonlinear Schrödinger type tetrahedron maps
Nuclear Physics B, 2020 This paper is concerned with the construction of new solutions in terms of birational maps to the functional tetrahedron equation and parametric tetrahedron equation.
S. Konstantinou-Rizos
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Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation
Advances in Mathematical Physics, 2021 In this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield its Darboux expression in additive form. The new linear
Irfan Mahmood, Muhammad Waseem
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Darboux transforms of Dupin surfaces [PDF]
Banach Center Publications, 2002 We present a Mobius invariant construction of the Darboux transformation for isothermic surfaces by the method of moving frames and use it to give a complete classification of the Darboux transforms of Dupin ...
MUSSO, EMILIO, NICOLODI L.
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A Five-Component Generalized mKdV Equation and Its Exact Solutions
Mathematics, 2020 In this paper, a 3 × 3 spectral problem is proposed and a five-component equation that consists of two different mKdV equations is derived. A Darboux transformation of the five-component equation is presented relating to the gauge transformations
Bo Xue, Huiling Du, Ruomeng Li
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On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation
Mathematics, 2019 A vector modified Yajima−Oikawa long-wave−short-wave equation is proposed using the zero-curvature presentation. On the basis of the Riccati equations associated with the Lax pair, a method is developed to construct multi-fold classical and ...
Xianguo Geng, Ruomeng Li
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Advances in Mathematical Physics, 2022 In this letter, we consider a new two-component system. By its reciprocal relation with the first negative flow in the AKNS hierarchy, we construct three Darboux-Bäcklund transformations for the new system and obtain some soliton-like solutions.
Shilong Huang, Hongmin Li
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