Results 1 to 10 of about 863 (58)
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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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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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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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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Proceedings of the London Mathematical Society, Volume 121, Issue 4, Page 954-1032, October 2020., 2020 Abstract I provide an explicit construction of spectral curves for the affine E8 relativistic Toda chain. Their closed‐form expression is obtained by determining the full set of character relations in the representation ring of E8 for the exterior algebra of the adjoint representation; this is in turn employed to provide an explicit construction of ...
Andrea Brini
wiley +1 more source
Partial Differential Equations in Applied Mathematics, 2020 In this article, we apply a direct influential approach namely enhanced modified simple equation (EMSE) method to integrate the Burgers–Huxley (BH) and FitzHugh–Nagumo (FHN) equations which explain nerve pulse propagation in nerve fibers, circuit theory ...
Md. Mamunur Roshid +3 more
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Recursion Operators and Frobenius Manifolds [PDF]
, 2012 In this note I exhibit a "discrete homotopy" which joins the category of F-manifolds to the category of Poisson-Nijenhuis manifolds, passing through the category of Frobenius ...
Magri, Franco
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By Magri's Theorem, Self-Dual Gravity is Completely Integrable [PDF]
, 2007 By Magri's theorem the bi-Hamiltonian structure of Plebanski's second heavenly equation proves that (anti)-self-dual gravity is a completely integrable system in four dimensions.Comment: This is a contribution to the Proc.
Nutku, Yavuz
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Singularity Analysis and Integrability of a Burgers-Type System of Foursov [PDF]
, 2011 We apply the Painleve test for integrability of partial differential equations to a system of two coupled Burgers-type equations found by Foursov, which was recently shown by Sergyeyev to possess infinitely many commuting local generalized symmetries ...
Sakovich, Sergei
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