Results 11 to 20 of about 9,686 (209)
Darboux transformation and exact solutions for a four-component Fokas–Lenells equation
Results in Physics, 2021 In the present paper, we introduce a 4 × 4 matrix spectral problem and derive a four-component Fokas–Lenells equation. N-fold Darboux transformations for the four-component Fokas–Lenells equation are constructed by using the gauge transformation between ...
Yihao Li +3 more
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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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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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Classification of Multidimensional Darboux Transformations: First Order and Continued Type [PDF]
, 2017 We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type.
Hobby, David, Shemyakova, Ekaterina
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Elementary Darboux Transformations and Factorization [PDF]
Theoretical and Mathematical Physics, 2005 10 ...
Musso, F., Shabat, A. B.
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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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