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Displaying 361 – 380 of 441

The generalized de Rham-Hodge theory aspects of Delsarte-Darboux type transformations in multidimension

Anatoliy Samoilenko, Yarema Prykarpatsky, Anatoliy Prykarpatsky (2005)

Open Mathematics

The differential-geometric and topological structure of Delsarte transmutation operators and their associated Gelfand-Levitan-Marchenko type eqautions are studied along with classical Dirac type operator and its multidimensional affine extension, related with selfdual Yang-Mills eqautions. The construction of soliton-like solutions to the related set of nonlinear dynamical system is discussed.

The geometry of dented pentagram maps

Boris Khesin, Fedor Soloviev (2016)

Journal of the European Mathematical Society

We propose a new family of natural generalizations of the pentagram map from 2D to higher dimensions and prove their integrability on generic twisted and closed polygons. In dimension $d$ there are $d - 1$ such generalizations called dented pentagram maps, and we describe their geometry, continuous limit, and Lax representations with a spectral parameter. We prove algebraic-geometric integrability of the dented pentagram maps in the 3D case and compare the dimensions of invariant tori for the dented maps...

The Hirota method and soliton solutions to the multidimensional nonlinear Schrödinger equation.

Borzykh, A.V. (2002)

Sibirskij Matematicheskij Zhurnal

The Kowalevski's top and the method of Syzygies

Franco Magri (2005)

Annales de l’institut Fourier

A new algorithm for finding separation coordinates is tested on the example of Kowalev ski’s top.

The lattice structure of connection preserving deformations for $q$ -Painlevé equations I.

Ormerod, Christopher M. (2011)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

The Lax integrable differential-difference dynamical systems on extended phase spaces.

Hentosh, Oksana Ye. (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

The Novikov-Veselov hierarchy of equations and integrable deformations of minimal Lagrangian tori in $ℂ P^{2}$ .

Mironov, A.E. (2004)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

The Painlevé III equation and the Iwasawa decomposition.

Alexander Bobenko, Alexander Its (1995)

Manuscripta mathematica

The Painlevé test and reducibility to the canonical forms for higher-dimensional soliton equations with variable-coefficients.

Kobayashi, Tadashi, Toda, Kouichi (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

The real-analytic solutions of the Abel functional equation

G. Belitskii, Yu. Lyubich (1999)

Studia Mathematica

For the Abel equation on a real-analytic manifold a dynamical criterion of solvability in real-analytic functions is proved.

The solution of general KdV equation in a class of steplike functions.

Khasanov, A.B., Urazboev, G.U. (2004)

Zapiski Nauchnykh Seminarov POMI

The spectral matrices of Toda solitons and the fundamental solution of some discrete heat equations

Luc Haine (2005)

Annales de l’institut Fourier

The Stieltjes spectral matrix measure of the doubly infinite Jacobi matrix associated with a Toda $g$ -soliton is computed, using Sato theory. The result is used to give an explicit expansion of the fundamental solution of some discrete heat equations, in a series of Jackson’s $q$ -Bessel functions. For Askey-Wilson type solitons, this expansion reduces to a finite sum.

The Spectrum of Jacobi Matrices.

Pierre van Moerbeke (1976)

Inventiones mathematicae

The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI

Henrik Aratyn, Johan van de LEUR (2005)

Annales de l’institut Fourier

Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension $μ$ , time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomonodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give...

The Theory of differential invariance and infinite dimensional Hamiltonian evolutions

Gloria Beffa (2000)

Banach Center Publications

In this paper we describe the close relationship between invariant evolutions of projective curves and the Hamiltonian evolutions of Adler, Gel'fand and Dikii. We also show how KdV evolutions are related as well to invariant evolutions of projective surfaces.

Currently displaying 361 – 380 of 441

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Displaying 361 – 380 of 441

The generalized de Rham-Hodge theory aspects of Delsarte-Darboux type transformations in multidimension

The geometry of dented pentagram maps

The Hirota method and soliton solutions to the multidimensional nonlinear Schrödinger equation.

The Kowalevski's top and the method of Syzygies

The lattice structure of connection preserving deformations for $q$ -Painlevé equations I.

The Lax integrable differential-difference dynamical systems on extended phase spaces.

The Novikov-Veselov hierarchy of equations and integrable deformations of minimal Lagrangian tori in $ℂ P^{2}$ .

The Painlevé III equation and the Iwasawa decomposition.

The Painlevé test and reducibility to the canonical forms for higher-dimensional soliton equations with variable-coefficients.

The real-analytic solutions of the Abel functional equation

The solution of general KdV equation in a class of steplike functions.

The spectral matrices of Toda solitons and the fundamental solution of some discrete heat equations

The Spectrum of Jacobi Matrices.

The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI

The Theory of differential invariance and infinite dimensional Hamiltonian evolutions

The theory of differential invariants and KDV hamiltonian evolutions

Time-like isothermic surfaces associated to Grassmannian systems.

Trajectoires bornées d'une particule soumise à un champ magnétique symétrique linéaire

Transformation operators for the perturbed Hill difference equation and one of their applications.

Transformations between surfaces in $m a t h b b R^{4}$ with flat normal and/or tangent bundles.

Currently displaying 361 – 380 of 441