Results 1 to 10 of about 1,801 (94)
The sixth Painleve equation arising from D_4^{(1)} hierarchy [PDF]
, 2006 The sixth Painleve equation arises from a Drinfel'd-Sokolov hierarchy associated with the affine Lie algebra of type D_4 by similarity reduction.
Carter R +10 more
arxiv +3 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
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
doaj +1 more source
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
semanticscholar +1 more source
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
semanticscholar +2 more sources
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
core +4 more sources