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A Method for Obtaining Darboux Transformations [PDF]
Journal of Nonlinear Mathematical Physics, 1998 In this paper we give a method to obtain Darboux transformations (DTs) of integrable equations. As an example we give a DT of the dispersive water wave equation. Using the Miura map, we also obtain the DT of the Jaulent-Miodek equation. \end{abstract}
Lu, Baoqun, He, Yong, Ni, Guangjiong
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Darboux transformations for differential operators on the superline
, 2015 We give a full description of Darboux transformations of any order for arbitrary (nondegenerate) differential operators on the superline. We show that every Darboux transformation of such operators factorizes into elementary Darboux transformations of ...
Hill, Sean +2 more
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Darboux transformation of symmetric Jacobi matrices and Toda lattices
Frontiers in Applied Mathematics and StatisticsLet J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively.
Ivan Kovalyov, Oleksandra Levina
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Deformed solitons of a typical set of (2+1)–dimensional complex modified Korteweg–de Vries equations
International Journal of Applied Mathematics and Computer Science, 2020 Deformed soliton solutions are studied in a typical set of (2+1)-dimensional complex modified Korteweg–de Vries (cmKdV) equations. Through constructing the determinant form of the n-fold Darboux transformation for these (2+1)-dimensional cmKdV equations,
Yuan Feng, Zhu Xiaoming, Wang Yulei
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Hearing the shape of a drum for light: isospectrality in photonics
Nanophotonics, 2021 The independent tailoring of wave quantities lays the foundation for controlling wave phenomena and designing wave devices. The concept of isospectrality, which suggests the existence of systems that provide identical spectra, has inspired a novel route ...
Park Seungkyun +4 more
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Physical Review LettersThe Optical Darboux Transformer is introduced as a photonic device which performs the Darboux transformation directly in the optical domain. This enables two major advances for signal processing based on the nonlinear Fourier transform: (i) the multiplexing of different solitonic waveforms corresponding to arbitrary number of discrete eigenvalues of ...
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Noncommutative bispectral Darboux transformations
Transactions of the American Mathematical Society, 2017 We prove a general theorem establishing the bispectrality of noncommutative Darboux transformations. It has a wide range of applications that establish bispectrality of such transformations for differential, difference and q q -difference operators with values in all noncommutative algebras. All known bispectral Darboux transformations
Geiger, J., Horozov, E., Yakimov, M.
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Supersymmetry and Darboux transformations
Journal of Physics: Conference Series, 2012 We study supersymmetry and Darboux transformations for generalized Schrodinger equations with a position-dependent mass and with linearly energy-dependent potentials. The formally adjoint generators of supersymmetry and two superpartner Hamiltonians are constructed and they close a quadratic pseudo-superalgebra for our class of equations.
A A Suzko, E Velicheva
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Darboux transformation for the modified Veselov-Novikov equation
, 2001 A Darboux transformation is constructed for the modified Veselov-Novikov equation.Comment: Latex file,8 pages, 0 ...
Bognadov L V +10 more
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The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1 [PDF]
Opuscula Mathematica, 2006 The structure properties of multidimensional Delsarte-Darboux transmutation operators in parametric functional spaces are studied by means of differential-geometric and topological tools.
Yarema A. Prykarpatsky +1 more
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