Results 41 to 50 of about 86,829 (231)
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
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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
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Integrability via geometry: dispersionless differential equations in three and four dimensions [PDF]
, 2019 We prove that the existence of a dispersionless Lax pair with spectral parameter for a nondegenerate hyperbolic second order partial differential equation (PDE) is equivalent to the canonical conformal structure defined by the symbol being Einstein-Weyl ...
Calderbank, David M. J. +1 more
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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
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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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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
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Lax Pairs for the Discrete Reduced Nahm Systems [PDF]
Mathematical Physics, Analysis and Geometry, 2021 We discretise the Lax pair for the reduced Nahm systems and prove its equivalence with the Kahan-Hirota-Kimura discretisation procedure. We show that these Lax pairs guarantee the integrability of the discrete reduced Nahm systems providing an invariant.
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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
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Higher dimensional Lax pairs of lower dimensional chaos and turbulence systems
, 2001 In this letter, a definition of the higher dimensional Lax pair for a lower dimensional system which may be a chaotic system is given. A special concrete (2+1)-dimensional Lax pair for a general (1+1)-dimensional three order autonomous partial ...
Ablowitz +9 more
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Lax pair for strings in Lunin-Maldacena background [PDF]
Journal of High Energy Physics, 2005 Recently Lunin and Maldacena used an SL(3,R) transformation of the AdS_5 x S^5 background to generate a supergravity solution dual to a so-called beta-deformation of N = 4 super Yang-Mills theory. We use a T-duality-shift-T-duality (TsT) transformation to obtain the beta-deformed background for real beta, and show that solutions of string theory ...
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