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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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NONLINEAR EQUATION WITH THE THIRD ORDER SCATTERING OPERATOR
Наука. Инновации. Технологии, 2022 Introduction: most of the differential equations associated with soliton mathematics are obtained using the Lax operator equation or the zero-curvature equation, which are the compatibility condition for a pair of linear differential systems. The case in
Olga Sergeevna Yanovskaya +1 more
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The Lax pairs for the Holt system [PDF]
Journal of Physics A: Mathematical and General, 1999 By using non-canonical transformation between the Holt system and the Henon-Heiles system the Lax pairs for all the integrable cases of the Holt system are constructed from the known Lax representations for the Henon-Heiles system.
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Weak Lax pairs for lattice equations [PDF]
Nonlinearity, 2012 We consider various 2D lattice equations and their integrability, from the point of view of 3D consistency, Lax pairs and Bäcklund transformations. We show that these concepts, which are associated with integrability, are not strictly equivalent. In the course of our analysis, we introduce a number of black and white lattice models, as well as variants
Hietarinta, Jarmo, Viallet, Claude
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Symmetries for the Semi-Discrete Lattice Potential Korteweg–de Vries Equation
MathematicsIn this paper, we prove that the isospectral flows associated with both the x-part and the n-part of the Lax pair of the semi-discrete lattice potential Korteweg–de Vries equation are symmetries of the equation.
Junwei Cheng, Xiang Tian
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Results in Physics, 2016 We demonstrate that the Darboux transformation in the paper “Soliton solutions by Darboux transformation and some reductions for a new Hamiltonian lattice hierarchy” [Phys. Scr.
Xi-Xiang Xu
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On some integrability aspects of the two-component Camassa–Holm equation
Partial Differential Equations in Applied Mathematics, 2022 The integrability of the two-component Camassa–Holm shallow water equation with the gravity acceleration points downwards and upwards is investigated by prolongation structure theory and the geometric approach of pseudo-spherical surfaces.
Deng-Shan Wang
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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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On the complete integrability of an equation having solitons but not known to have a Lax pair
International Journal of Mathematics and Mathematical Sciences, 1986 It is usually assumed that a system having N-soliton solutions is completely integrable. Here we have analyzed a set of equations occuring in case of capillary gravity waves.
A. Roychowdhury, G. Mahato
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Binary Nonlinearization of Lax Pairs
, 1996 8 pages, latex, to appear in the Proceedings of Nonlinear Physics ...
Ma, Wen-Xiu, Fuchssteiner, Benno
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