Results 21 to 30 of about 1,134 (216)
Solution of High-Order Nonlinear Integrable Systems Using Darboux Transformation
Axioms, 2023 The 4×4 trace-free complex matrix set is introduced in this study. By using it, we are able to create a novel soliton hierarchy that is reduced to demonstrate its bi-Hamiltonian structure.
Xinhui Wu, Jiawei Hu, Ning Zhang
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Darboux transformation of symmetric Jacobi matrices and Toda lattices [PDF]
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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Discrete Dynamics in Nature and Society, 2018 An integrable family of the different-difference equations is derived from a discrete matrix spectral problem by the discrete zero curvature representation. Hamiltonian structure of obtained integrable family is established.
Xi-Xiang Xu, Meng Xu
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Darboux transformation and solution of the modified Korteweg–de Vries equation
Қарағанды университетінің хабаршысы. Математика сериясы, 2015 Darboux transformation and a comprehensive approach to construct exact solutions of the nonlinear differential equation are counted. It is applied to construct the explicit solutions of the (2+1)-dimensional modified Korteweg-de Vries (KdV) equation. In
G. Kemelbekova +3 more
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Applied Mathematics Letters, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Schulze-Halberg, Axel
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A modified Suris hierarchy and N-fold Darboux -Bäcklund transformation
Partial Differential Equations in Applied Mathematics, 2022 A modified Suris hierarchy is derived by discrete zero curvature equation. Bi-Hamiltonian structure of the whole hierarchy is established through the discrete trace identity. And we prove that the obtained hierarchy is Liouville integrable.
Ning Zhang, Xi-Xiang Xu
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The stability of bright–dark solitons in defocusing coupled nonlinear Schrödinger equation
Partial Differential Equations in Applied Mathematics, 2022 The Darboux transformation is a classical method to generate the solitonic solutions for the integrable equations. In this work, we develop the Darboux transformation to analyze the spectral stability of bright–dark soliton for defocusing coupled ...
Liming Ling, Xuan Sun
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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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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 unified approach to Darboux transformations [PDF]
Inverse Problems, 2009 We analyze a certain class of integral equations related to Marchenko equations and Gel'fand-Levitan equations associated with various systems of ordinary differential operators. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution.
TUNCAY AKTOSUN +1 more
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