Results 41 to 50 of about 1,858,479 (279)
Quantum line operators from Lax pairs [PDF]
Journal of Mathematical Physics, 2020 Motivated by the realization of the Yang–Baxter equation of 2D integrable models in the 4D gauge theory of Costello–Witten–Yamazaki (CWY), we study the embedding of integrable 2D Toda field models inside this construction. This is done by using the Lax formulation of 2D integrable systems and by thinking of the standard Lax pair L± in terms of ...
openaire +3 more sources
On integrability of 2-dimensional σ-models of Poisson-Lie type
Journal of High Energy Physics, 2017 We describe a simple procedure for constructing a Lax pair for suitable 2- dimensional σ-models appearing in Poisson-Lie T ...
Pavol Ševera
doaj +1 more source
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
doaj +1 more source
Integrable three-body systems with distinct two-body forces [PDF]
, 1991 Translationally invariant one-dimensional three-body systems with mutually different pair potentials are derived that possess a third constant of motion, both classically and quantum-mechanically; a Lax pair is given, and all (even) regular solutions of ...
Hoppe, J., Theisen, S.
core +1 more source
Lax Pair for a Novel Two-Dimensional Lattice [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 In paper by I.T. Habibullin and our joint paper the algorithm for classification of integrable equations with three independent variables was proposed. This method is based on the requirement of the existence of an infinite set of Darboux integrable reductions and on the notion of the characteristic Lie-Rinehart algebras. The method was applied for the
openaire +3 more sources
The Derivation of a Fifth-Order Equation via the Lax and the Alternate Lax Methods
Cumhuriyet Science JournalWe present the derivation of a fifth-order integrable nonlinear partial differential equation via the Lax method and the alternate Lax method in the continuous case.
Mehmet Ünlü
doaj +1 more source
Mathematics, 2019 In this paper, the Lax pair of the modified nonlinear Schrödinger equation (mNLS) is derived by means of the prolongation structure theory. Based on the obtained Lax pair, the mNLS equation on the half line is analyzed with the assistance of Fokas ...
Tongshuai Liu, Huanhe Dong
doaj +1 more source
On the Propagation Model of Two-Component Nonlinear Optical Waves
Axioms, 2023 Currently, two-component integrable nonlinear equations from the hierarchies of the vector nonlinear Schrodinger equation and the vector derivative nonlinear Schrödinger equation are being actively investigated.
Aleksandr O. Smirnov, Eugeni A. Frolov
doaj +1 more source
Geometry of Lax pairs: particle motion and Killing-Yano tensors
, 2012 A geometric formulation of the Lax pair equation on a curved manifold is studied using phase space formalism. The corresponding (covariantly conserved) Lax tensor is defined and the method of generation of constants of motion from it is discussed.
Cariglia, Marco +3 more
core +1 more source
Lagrangian and Hamiltonian structures in an integrable hierarchy and space–time duality
Nuclear Physics B, 2016 We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution equation (NLEE) in the hierarchy, dual integrable structures are characterized ...
Jean Avan +3 more
doaj +1 more source