Results 91 to 100 of about 1,595,275 (210)
Bäcklund--Darboux transformations in Sato's Grassmannian
, 1996 13 pages, LaTeX2e, uses amsfonts.sty and latexsym.sty, no ...
Bakalov, B., Horozov, E., Yakimov, M.
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Darboux transformation for the discrete Schrödinger equation
Electronic Journal of Differential Equations, 2018 The discrete Schrödinger 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. The Darboux transformation formulas are derived from first principles showing how the potential and the wavefunction change when a bound state is added to or removed ...
Tuncay Aktosun +2 more
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AxiomsThe paper reveals some remarkable form-invariance features of the ‘Jacobi-reference’ canonical Sturm–Liouville equation (CSLE) in the particular case of the density function with the simple pole at the origin.
Gregory Natanson
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Restricted Flows and the Soliton Equation with Self-Consistent Sources
Symmetry, Integrability and Geometry: Methods and Applications, 2006 The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Bäcklund transformation for the restricted flows (by V.B. Kuznetsov et al.
Runliang Lin, Haishen Yao, Yunbo Zeng
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Rogue Wave Solutions to Integrable System by Darboux Transformation
, 2014 The Darboux transformation is one of the main techniques for finding solutions of integrable equations. The Darboux transformation is not only powerful in the construction of muilti-soliton solutions, recently, it is found that the Darboux transformation,
Kou, Xin
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MathematicsThis paper conducts an in-depth study on the self-similar transformation, Darboux transformation, and the excitation and propagation characteristics of high-order bright–dark rogue wave solutions in the (2+1)-dimensional variable-coefficient Zakharov ...
Hangwei Zhang +3 more
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Integral transformation and Darboux transformation
, 2009 We review Darboux-Crum transformation of Heun's differential equation. By rewriting an integral transformation of Heun's differential equation into a form of elliptic functions, we see that the integral representation is a generalization of Darboux-Crum transformation. We also consider conservation of monodromy with respect to the transformations.
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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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Transactions of the American Mathematical Society, 1967 Bruckner, A. M., Bruckner, J. B.
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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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