An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type
Sign Up to like & getrecommendations! Published in 2018 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2018.09.023
Abstract: Abstract The Novikov equation is an integrable analogue of the Camassa–Holm equation with a cubic (rather than quadratic) nonlinear term. Both these equations support a special family of weak solutions called multipeakon solutions. In this… read more here.
Keywords: novikov equation; equation; toda lattice; finite toda ... See more keywords
Algebraic complete integrability of the c2(1) Toda lattice
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2018.09.008
Abstract: Abstract The aim of this paper is to study the algebraic complete integrability of an integrable system, namely the Toda lattice associated to the twisted affine Lie algebra c 2 ( 1 ) . We… read more here.
Keywords: integrability toda; algebraic complete; toda lattice; complete integrability ... See more keywords
The resolutions of the singular loci of the Toda lattice on the split and connected reductive Lie groups
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2019.103558
Abstract: Abstract In this paper we study the resolution of the singular loci of the generalized Toda lattice on the flag manifold by using blow-up. We define the gauge symmetry of the Weyl group on the… read more here.
Keywords: toda lattice; resolutions singular; singular loci; flag manifold ... See more keywords
On the mean density of states of some matrices related to the beta ensembles and an application to the Toda lattice
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0076539
Abstract: In this paper, we study tridiagonal random matrix models related to the classical β-ensembles (Gaussian, Laguerre, and Jacobi) in the high-temperature regime, i.e., when the size N of the matrix tends to infinity with the… read more here.
Keywords: mean density; states matrices; toda lattice; density states ... See more keywords
Fifty years of the finite nonperiodic Toda lattice: a geometric and topological viewpoint
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/aacecf
Abstract: In 1967, Japanese physicist Morikazu Toda published a pair of seminal papers in the Journal of the Physical Society of Japan that exhibited soliton solutions to a chain of particles with nonlinear interactions between nearest… read more here.
Keywords: toda lattice; toda; geometric topological; finite nonperiodic ... See more keywords
Solitons of the (2+2)-dimensional Toda lattice
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/aaea08
Abstract: We use the generalized Cauchy matrix approach to derive the N-soliton solutions for the (2+2)-dimensional Toda lattice. read more here.
Keywords: toda lattice; dimensional toda; solitons dimensional;
Toda lattice hierarchy and trigonometric Ruijsenaars–Schneider hierarchy
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/ab520c
Abstract: We consider solutions of the 2D Toda lattice hierarchy which are trigonometric functions of the ``zeroth'' time $t_0=x$. It is known that their poles move as particles of the trigonometric Ruijsenaars-Schneider model. We extend this… read more here.
Keywords: toda lattice; lattice hierarchy; hierarchy trigonometric; ruijsenaars schneider ... See more keywords
On a Toda lattice hierarchy: Lax pair, integrable symplectic map and algebraic–geometric solution
Sign Up to like & getrecommendations! Published in 2018 at "Modern Physics Letters B"
DOI: 10.1142/s021798491850344x
Abstract: A Toda lattice hierarchy is studied by introducing a new spectral problem which is a discrete counterpart of the generalized Kaup–Newell spectral problem. Based on the Lenard recursion equation, La... read more here.
Keywords: toda lattice; hierarchy lax; lax pair; pair integrable ... See more keywords
A Relativistic Toda Lattice Hierarchy, Discrete Generalized (m, 2N-m)-Fold Darboux Transformation and Diverse Exact Solutions
Sign Up to like & getrecommendations! Published in 2021 at "Symmetry"
DOI: 10.3390/sym13122315
Abstract: This paper investigates a relativistic Toda lattice system with an arbitrary parameter that is a very remarkable generalization of the usual Toda lattice system, which may describe the motions of particles in lattices. Firstly, we… read more here.
Keywords: lattice; toda lattice; darboux transformation; exact solutions ... See more keywords
Continuous Limit, Rational Solutions, and Asymptotic State Analysis for the Generalized Toda Lattice Equation Associated with 3 × 3 Lax Pair
Sign Up to like & getrecommendations! Published in 2022 at "Symmetry"
DOI: 10.3390/sym14050920
Abstract: Discrete integrable nonlinear differential difference equations (NDDEs) have various mathematical structures and properties, such as Lax pair, infinitely many conservation laws, Hamiltonian structure, and different kinds of symmetries, including Lie point symmetry, generalized Lie bäcklund… read more here.
Keywords: generalized toda; equation; toda lattice; lax pair ... See more keywords