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Related papers: Lax pair tensors in arbitrary dimensions

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In this paper a list of $R$-matrices on a certain coupled Lie algebra is obtained. With one of these $R$-matrices, we construct infinitely many bi-Hamiltonian structures for each of the two-component BKP and the Toda lattice hierarchies. We…

Exactly Solvable and Integrable Systems · Physics 2013-05-07 Chao-Zhong Wu

We construct the recursion operators for the non-commutative Burgers equations using their Lax operators. We investigate the existence of any integrable mixed version of left- and right-handed Burgers equations on higher symmetry grounds.

Exactly Solvable and Integrable Systems · Physics 2015-05-13 M. Gurses , A. Karasu , R. Turhan

In this paper, we construct a Lax pair for the classical hyperbolic van Diejen system with two independent coupling parameters. Built upon this construction, we show that the dynamics can be solved by a projection method, which in turn…

Mathematical Physics · Physics 2017-07-07 B. G. Pusztai , T. F. Gorbe

We find a Lax pair for the geometrically exact discrete Hamiltonian equations for the discrete elastic rod. This is paper III of a series.

Exactly Solvable and Integrable Systems · Physics 2008-06-24 Yaoming Shi , W. M. McClain , J. E. Hearst

We review the recent approach to the construction of (3+1)-dimensional integrable dispersionless partial differential systems based on their contact Lax pairs and the related $R$-matrix theory for the Lie algebra of functions with respect…

Exactly Solvable and Integrable Systems · Physics 2019-01-17 M. Blaszak , A. Sergyeyev

Given a Lax system of equations with the spectral parameter on a Riemann surface we construct a projective unitary representation of the Lie algebra of Hamiltonian vector fields by Knizhnik-Zamolodchikov operators. This provides a…

Representation Theory · Mathematics 2014-06-20 Oleg K. Sheinman

This note constructs completely integrable convex Hamiltonians on the cotangent bundle of certain k-dimensional torus bundles over an l-dimensional torus. A central role is played by the Lax representation of a Bogoyavlenskij-Toda lattice.…

Exactly Solvable and Integrable Systems · Physics 2015-05-13 Leo T. Butler

We consider 1+1 - dimensional non-homogeneous systems of hydrodynamic type that possess Lax representations with movable singularities. We present a construction, which provides a wide class of examples of such systems with arbitrary number…

Exactly Solvable and Integrable Systems · Physics 2015-06-05 A. V. Odesskii , V. V. Sokolov

It is quite basic in integrable systems to deriving Lax equations from bilinear equations. For multi--component KP theory, corresponding Lax structures are mainly constructed by matrix pseudo-differential operators for fixed discrete…

Exactly Solvable and Integrable Systems · Physics 2024-08-01 Tongtong Cui , Jinbiao Wang , Wenqi Cao , Jipeng Cheng

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the possible reductions of the Poisson tensors, the vector field and its Hamiltonian functions on a four-dimensional space. We…

Exactly Solvable and Integrable Systems · Physics 2009-11-07 C. Morosi , G. Tondo

We consider a Lax pair found by Xia, Qiao and Zhou for a family of two-component analogues of the Camassa-Holm equation, including an arbitrary function $H$, and show that this apparent freedom can be removed via a combination of a…

Exactly Solvable and Integrable Systems · Physics 2018-05-10 Mike Hay , Andrew N. W. Hone , Vladimir S. Novikov , Jing Ping Wang

In a previous article [N. Delice, F.W. Nijhoff and S. Yoo-Kong, J. Phys. A: Math. Theor. 48(3) (2015), 035206] a novel class of elliptic Lax pairs for integrable lattice equations was introduced. The present article proposes a…

Exactly Solvable and Integrable Systems · Physics 2016-05-04 Frank Nijhoff , Neslihan Delice

It is shown that the Zakharov-Mihailov (ZM) Lagrangian structure for integrable nonlinear equations derived from a general class of Lax pairs possesses a Lagrangian multiform structure. We show that, as a consequence of this multiform…

Mathematical Physics · Physics 2019-07-18 D. G. Sleigh , F. W. Nijhoff , V. Caudrelier

A new one-dimensional model, the multicomponent Calogero model of $B_N$-type confined in the harmonic potential, is introduced. The Lax pair of this model is determined, and then a set of functionally independent conserved operators are…

Condensed Matter · Physics 2009-10-28 Takashi Yamamoto

A general elliptic $N\times N$ matrix Lax scheme is presented, leading to two classes of elliptic lattice systems, one which we interpret as the higher-rank analogue of the Landau-Lifschitz equations, while the other class we characterize…

Exactly Solvable and Integrable Systems · Physics 2015-06-19 N. Delice , F. W. Nijhoff , S. Yoo-Kong

We report a two-parametric irreducible infinitely dimensional representation of the Lax integrability condition for the fermi Hubbard chain. Besides being of fundamental interest, hinting on possible novel quantum symmetry of the model, our…

Mathematical Physics · Physics 2015-04-28 Vladislav Popkov , Tomaz Prosen

We present general formulas for transverse and transverse-traceless (TT) symmetric tensors in flat spaces. TT tensors in conformally flat spaces can be obtained by means of a conformal transformation.

General Relativity and Quantum Cosmology · Physics 2020-02-24 J. Tafel

We produce a hierarchiy of integrable equations by systematically adding terms to the Lax pair for the lattice modified KdV equation. The equations in the hierarchy are related to one aonother by recursion relations. These recursion…

Exactly Solvable and Integrable Systems · Physics 2015-06-05 Mike Hay

We present a simple novel construction of recursion operators for integrable multidimensional dispersionless systems that admit a Lax pair whose operators are linear in the spectral parameter and do not involve the derivatives with respect…

Analysis of PDEs · Mathematics 2017-09-29 A. Sergyeyev

In this work, we continue the development of methods for constructing Lax pairs and recursion operators for nonlinear integrable hyperbolic equations of soliton type, previously proposed in the work of Habibullin et al. (2016 {\it J. Phys.…

Exactly Solvable and Integrable Systems · Physics 2024-07-01 K I Faizulina , A R Khakimova