Results 101 to 110 of about 1,134 (216)
Transformation Groups and the Method of Darboux
, 2021 In the study of partial differential equations (PDE), one is often concerned as to whether or not explicit solutions can be obtained via various integration techniques.
Ashley, Brandon P.
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The Multidimensional Darboux Transformation
, 2007 . 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.
Artemio González-López, Niky Kamran
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Binary Darboux transformation for the coupled Sasa-Satsuma equations
, 2017 The binary Darboux transformation method is applied to the coupled Sasa-Satsuma equations, which can be used to describe the propagation dynamics of femtosecond vector solitons in the birefringent fibers with third-order dispersion, self-steepening, and ...
Wang, Yue +5 more
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Explicit Solutions and Conservation Laws for a New Integrable Lattice Hierarchy
Complexity, 2019 An integrable lattice hierarchy is derived on the basis of a new matrix spectral problem. Then, some properties of this hierarchy are shown, such as the Liouville integrability, the bi-Hamiltonian structure, and infinitely many conservation laws.
Qianqian Yang, Qiulan Zhao, Xinyue Li
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Fractional Darboux Transformations
, 2002 In this paper we utilize the covariance of Ricatti equation with respect to linear fractional transformations to define classes of conformally equivalent second order differential equations. This motivates then the introduction of fractional Darboux transformations which can be recognized also as generalized Cole-Hopf transformations.
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Transactions of the American Mathematical Society, 1967 Bruckner, A. M., Bruckner, J. B.
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Bäcklund Transformations for the Trigonometric Gaudin Magnet
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We construct a Bäcklund transformation for the trigonometric classical Gaudin magnet starting from the Lax representation of the model. The Darboux dressing matrix obtained depends just on one set of variables because of the so-called spectrality ...
Federico Zullo, Orlando Ragnisco
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Abstract and Applied Analysis, 2014 We mainly investigate the generalized nonlinear Schrödinger-Maxwell-Bloch system which governs the propagation of optical solitons in nonlinear erbium-doped fibers with higher-order effects.
Rui Guo, Hui-Qin Hao, Xiao-Song Gu
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Darboux transformations and random point processes
, 2014 In this paper we describe a general method to derive formulas relating the gap probability of some classical determinantal random point process (Airy, Pearcey and Hermite) with the gap probability of the processes related to the same kernels with "wanderers", "inliers" and "outliers".
Bertola, M., Cafasso, M.
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Darboux transformation for the discrete Schrodinger equation
Electronic Journal of Differential Equations, 2019 The discrete Schrodinger equation on a half-line lattice with the Dirichlet boundary condition is considered when the potential is real valued, is summable, and has a finite first moment.
Tuncay Aktosun +2 more
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