Results 21 to 30 of about 582,779 (212)
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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Advances in Mathematical Physics, 2022 In this letter, we consider a new two-component system. By its reciprocal relation with the first negative flow in the AKNS hierarchy, we construct three Darboux-Bäcklund transformations for the new system and obtain some soliton-like solutions.
Shilong Huang, Hongmin Li
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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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Darboux transformation: new identities [PDF]
Physica Scripta, 2019 Abstract This letter reports some new identities for multisoliton potentials that are based on the explicit representation provided by the Darboux matrix. These identities can be used to compute the complex gradient of the energy content of the tail of the profile with respect to the discrete eigenvalues and the norming constants. The
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A Comprehensive Study of the Complex mKdV Equation through the Singular Manifold Method
Mathematics, 2023 In this paper, we introduce a modification of the Singular Manifold Method in order to derive the associated spectral problem for a generalization of the complex version of the modified Korteweg–de Vries equation.
Paz Albares, Pilar G. Estévez
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D-Modules and Darboux Transformations
Letters in Mathematical Physics, 1998 A method of G. Wilson for generating commutative algebras of ordinary differential operators is extended to higher dimensions. Our construction, based on the theory of D-modules, leads to a new class of examples of commutative rings of partial differential operators with rational spectral varieties.
Berest, Yu., Kasman, A.
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Minimal Darboux transformations [PDF]
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2016 9 pages, 2 ...
Hertrich-Jeromin, Udo, Honda, Atsufumi
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MKdV方程和SG方程的可积曲面的构造(Conformation of soliton surfaces of MKdV equation and SG equation)
Zhejiang Daxue xuebao. Lixue ban, 2010 The soliton solutions and the soliton surfaces of Modified Korteweg-de Vries equation (MKdV) and Sine-Gordon (SG) equation by the n-fold Darboux transformation are given out.
ZHANGLing(张玲), DINGNan(丁楠)
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Quantum reference frames: derivation of perspective-dependent descriptions via a perspective-neutral structure [PDF]
Quantum, 2023 In standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized through finite-
Viktor Zelezny
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