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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
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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
Kuznetsova, Maria N.
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Lax pairs for deformed Minkowski spacetimes [PDF]
Journal of High Energy Physics, 2016 We proceed to study Yang-Baxter deformations of 4D Minkowski spacetime based on a conformal embedding. We first revisit a Melvin background and argue a Lax pair by adopting a simple replacement law invented in 1509.00173. This argument enables us to deduce a general expression of Lax pair.
Kyono, Hideki +2 more
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Lax Pairs for Linear Hamiltonian Systems [PDF]
Siberian Mathematical Journal, 2019 18 p., to appear in Sib.
Zheglov, A. B., Osipov, D. V.
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Similarity Analysis of Lax Pairs for a Class of Nonlinear Evolution Equations. [PDF]
The Egyptian International Journal of Engineering Sciences and TechnologyThe similarity transformation (ST) method is applied to reduce the Lax pair for some nonlinear partial differential equations (NLPDEs) into a system of ordinary differential equations (ODEs) to obtain its similarity solutions.
Shaimaa Ahmed, Samah Mabrouk
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Lax Pairs for the Modified KdV Equation
Axioms, 2023 Multi-parameter families of Lax pairs for the modified Korteweg-de Vries (mKdV) equation are defined by applying a direct method developed in the present study. The gauge transformations, converting the defined Lax pairs to some simpler forms, are found. The direct method and its possible applications to other types of evolution equations are discussed.
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Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax Pairs
Journal of Applied Mathematics, 2014 With the aid of symbolic computation, we obtain the symmetry transformations of the (2 + 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation by Lou’s direct method which is based on Lax pairs. Moreover, we use the classical Lie group method
Na Lv, Xuegang Yuan, Jinzhi Wang
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Lax pairs for new ZN-symmetric coset σ-models and their Yang-Baxter deformations
Nuclear Physics B, 2022 Two-dimensional σ-models with ZN-symmetric homogeneous target spaces have been shown to be classically integrable when introducing WZ-terms in a particular way. This article continues the search for new models of this type now allowing some kinetic terms
David Osten
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Lax pairs for integrable lattice systems [PDF]
Journal of Mathematical Physics, 1999 This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes the features that are needed to obtain equations which are local on the spatial lattice.
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Time-like boundary conditions in the NLS model
Nuclear Physics B, 2019 We focus on the non-linear Schrödinger model and we extend the notion of space-time dualities in the presence of integrable time-like boundary conditions.
Anastasia Doikou +2 more
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