Results 1 to 10 of about 76 (35)
The nonlinear Schr\"odinger equation with forcing involving products of eigenfunctions [PDF]
Open Communications in Nonlinear Mathematical Physics, 2022 We elaborate on a new methodology, which starting with an integrable evolution equation in one spatial dimension, constructs an integrable forced version of this equation.
A. S. Fokas, A. Latifi
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Hamiltonian structures for integrable hierarchies of Lagrangian PDEs [PDF]
Open Communications in Nonlinear Mathematical Physics, 2021 Many integrable hierarchies of differential equations allow a variational description, called a Lagrangian multiform or a pluri-Lagrangian structure. The fundamental object in this theory is not a Lagrange function but a differential $d$-form that is ...
Mats Vermeeren
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Inverse spectral problem for Jacobi operators and Miura transformation
Concrete Operators, 2021 We study a Miura-type transformation between Kac - van Moerbeke (Volterra) and Toda lattices in terms of the inverse spectral problem for Jacobi operators, which appear in the Lax representation for such systems.
Osipov Andrey
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Open Mathematics, 2023 In this article, the coupled matrix nonlinear Schrödinger (NLS) type equations are gauge equivalent to the equation of Schrödinger flow from R1{{\mathbb{R}}}^{1} to complex Grassmannian manifold G˜n,k=GL(n,C)∕GL(k,C)×GL(n−k,C),{\widetilde{G}}_{n,k}={\rm ...
Zhong Shiping, Zhao Zehui, Wan Xinjie
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Complex Lagrangians in a hyperKähler manifold and the relative Albanese
Complex Manifolds, 2020 Let M be the moduli space of complex Lagrangian submanifolds of a hyperKähler manifold X, and let ω̄ : 𝒜̂ → M be the relative Albanese over M. We prove that 𝒜̂ has a natural holomorphic symplectic structure.
Biswas Indranil +2 more
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Higher-Order Rogue Wave and Rational Soliton Solutions of Discrete Complex mKdV Equations
East Asian Journal on Applied Mathematics, 2018 The generalised perturbation (n, N − n)-fold Darboux transformation is used to derive new higher-order rogue wave and rational soliton solutions of the discrete complex mKdV equations.
Xiaoyong Wen
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The application of trigonal curve theory to the second-order Benjamin-Ono hierarchy
Advances in Differential Equations, 2014 By introducing two sets of Lenard recursion equations, the second-order Benjamin-Ono hierarchy is proposed. In view of the characteristic polynomial of Lax matrix, a trigonal curve of arithmetic genus m−1 is deduced.
G. He, Lin He
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Bi-integrable and tri-integrable couplings of a soliton hierarchy associated with SO(4)
Open Mathematics, 2017 In our paper, the theory of bi-integrable and tri-integrable couplings is generalized to the discrete case. First, based on the six-dimensional real special orthogonal Lie algebra SO(4), we construct bi-integrable and tri-integrable couplings associated ...
Zhang Jian, Zhang Chiping, Cui Yunan
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Bi-Hamiltonian Structures on the Tangent Bundle to a Poisson Manifold
Journal of Geometry and Symmetry in Physics, 2019 Communicated by Alexandar B. Yanovski Abstract. In the case when M is equipped with a bi-Hamiltonian structure (M,π1, π2) we show how to construct family of Poisson structures on the tangent bundle TM to a Poisson manifold.
A. Dobrogowska +2 more
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About seismic tomography algorithm in the prediction of geological dislocations in coal seams
Горные науки и технологии, 2018 An algorithm for processing of crosshole seismic survey data enabling recognizing the type and evaluate the characteristics of geological anomalies using a system of criteria is described.
A. V. Antsiferov +4 more
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