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$𝒟$ -bundles and integrable hierarchies

David Ben-Zvi, Thomas Nevins (2011)

Journal of the European Mathematical Society

We study the geometry of $𝒟$ -bundles—locally projective $𝒟$ -modules—on algebraic curves, and apply them to the study of integrable hierarchies, specifically the multicomponent Kadomtsev–Petviashvili (KP) and spin Calogero–Moser (CM) hierarchies. We show that KP hierarchies have a geometric description as flows on moduli spaces of $𝒟$ -bundles; in particular, we prove that the local structure of $𝒟$ -bundles is captured by the full Sato Grassmannian. The rational, trigonometric, and elliptic solutions of KP...

A Bäcklund transformation for the Burgers hierarchy.

Cao, Xifang, Xu, Chuanyou (2010)

Abstract and Applied Analysis

A critical phenomenon in solitonic Ising chains.

Loutsenko, Igor M., Spiridonov, Vyacheslav P. (2007)

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

A differential geometric setting for dynamic equivalence and dynamic linearization

Jean-Baptiste Pomet (1995)

Banach Center Publications

This paper presents an (infinite-dimensional) geometric framework for control systems, based on infinite jet bundles, where a system is represented by a single vector field and dynamic equivalence (to be precise: equivalence by endogenous dynamic feedback) is conjugation by diffeomorphisms. These diffeomorphisms are very much related to Lie-Bäcklund transformations. It is proved in this framework that dynamic equivalence of single-input systems is the same as static equivalence.

A discrete variational approach for investigation of stationary localized states in a discrete nonlinear Schrödinger equation, named IN-DNLS.

Kundu, K. (2005)

International Journal of Mathematics and Mathematical Sciences

A dynamical system connected with inhomogeneous 6-vertex model

И. Г. Корепанов (1994)

Zapiski naucnych seminarov POMI

A generalised Hopf algebra for solitons.

Al-Solamy, Falleh R., Beggs, Edwin J. (2002)

International Journal of Mathematics and Mathematical Sciences

A generalization for Peakon's solitary wave and Camassa-Holm equation.

Boldea, Costin-Radu (1997)

General Mathematics

A gentle (without chopping) approach to the full Kostant-Toda lattice.

Damianou, Pantelis A., Magri, Franco (2005)

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

A global factorization theorem for the ZS-AKNS system.

Wu, Derchyi (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

A Hopf bifurcation of interfaces in a Dirichlet problem.

Ham, YoonMee, Lee, Sang-Gu (1999)

Southwest Journal of Pure and Applied Mathematics [electronic only]

A KAM theorem for infinite-dimensional discrete systems.

Perfetti, Paolo (2003)

Mathematical Physics Electronic Journal [electronic only]

A look on some results about Camassa–Holm type equations

Igor Leite Freire (2021)

Communications in Mathematics

We present an overview of some contributions of the author regarding Camassa--Holm type equations. We show that an equation unifying both Camassa--Holm and Novikov equations can be derived using the invariance under certain suitable scaling, conservation of the Sobolev norm and existence of peakon solutions. Qualitative analysis of the two-peakon dynamics is given.

A new hierarchy of integrable system of $1 + 2$ dimensions: from Newton's law to generalized Hamiltonian system. II.

Huang, Xuncheng, Tu, Guizhang (2006)

International Journal of Mathematics and Mathematical Sciences

A note on the rotationally symmetric SO(4) Euler rigid body.

Falqui, Gregorio (2007)

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

A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation.

Hoel, Hakon A. (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

A recursion operator for the universal hierarchy equation via Cartan’s method of equivalence

Oleg Morozov (2014)

Open Mathematics

We apply Cartan’s method of equivalence to find a Bäcklund autotransformation for the tangent covering of the universal hierarchy equation. The transformation provides a recursion operator for symmetries of this equation.

Currently displaying 1 – 20 of 440

Page 1 Next

Displaying 1 – 20 of 440

$𝒟$ -bundles and integrable hierarchies

A Bäcklund transformation for the Burgers hierarchy.

A critical phenomenon in solitonic Ising chains.

A differential geometric setting for dynamic equivalence and dynamic linearization

A discrete variational approach for investigation of stationary localized states in a discrete nonlinear Schrödinger equation, named IN-DNLS.

A dynamical system connected with inhomogeneous 6-vertex model

A generalised Hopf algebra for solitons.

A generalization for Peakon's solitary wave and Camassa-Holm equation.

A gentle (without chopping) approach to the full Kostant-Toda lattice.

A global factorization theorem for the ZS-AKNS system.

A Hopf bifurcation of interfaces in a Dirichlet problem.

A KAM theorem for infinite-dimensional discrete systems.

A look on some results about Camassa–Holm type equations

A new hierarchy of integrable system of $1 + 2$ dimensions: from Newton's law to generalized Hamiltonian system. II.

A note on the rotationally symmetric SO(4) Euler rigid body.

A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation.

A recursion operator for the universal hierarchy equation via Cartan’s method of equivalence

A special case of the Garnier system, $(1, 4)$ -polarized abelian surfaces and their moduli

A survey of Nambu-Poisson geometry.

A survey on Nambu-Poisson brackets.

Currently displaying 1 – 20 of 440