English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  "Riemann equations" in bidifferential calculus

Chvartatskyi, O., Müller-Hoissen, F., & Stoilov, N. (2015). "Riemann equations" in bidifferential calculus. Journal of Mathematical Physics, 56(10): 103512. doi:10.1063/1.4934238.

Item is

Basic

show hide
Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-5B40-1 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-C318-5
Genre: Journal Article

Files

show Files

Locators

show

Creators

show
hide
 Creators:
Chvartatskyi, Oleksandr1, 2, Author              
Müller-Hoissen, Folkert1, Author              
Stoilov, Nikola1, 2, Author              
Affiliations:
1Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063285              
2Mathematisches Institut, Georg-August-Universität Göttingen, ou_persistent22              

Content

show
hide
Free keywords: -
 Abstract: We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential calculus, we obtain a variety of equations, including a semi-discrete and a fully discrete version of the matrix Riemann equation. A corresponding universal solution-generating method then either yields a (continuous or discrete) Cole-Hopf transformation, or leaves us with the problem of solving Riemann equations (hence an application of the hodograph method). If the bidifferential calculus extends to second order, solutions of a system of "Riemann equations" are also solutions of an equation that arises, on the universal level of bidifferential calculus, as an integrability condition. Depending on the choice of bidifferential calculus, the latter can represent a number of prominent integrable equations, like self-dual Yang-Mills, as well as matrix versions of the two-dimensional Toda lattice, Hirota’s bilinear difference equation, (2+1)-dimensional Nonlinear Schrödinger (NLS), Kadomtsev-Petviashvili (KP) equation, and Davey-Stewartson equations. For all of them, a recent (non-isospectral) binary Darboux transformation result in bidifferential calculus applies, which can be specialized to generate solutions of the associated "Riemann equations." For the latter, we clarify the relation between these specialized binary Darboux transformations and the aforementioned solution-generating method. From (arbitrary size) matrix versions of the "Riemann equations" associated with an integrable equation, possessing a bidifferential calculus formulation, multi-soliton-type solutions of the latter can be generated. This includes "breaking" multi-soliton-type solutions of the self-dual Yang-Mills and the (2+1)-dimensional NLS equation, which are parametrized by solutions of Riemann equations.

Details

show
hide
Language(s): eng - English
 Dates: 2015-10-262015-10
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1063/1.4934238
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: Journal of Mathematical Physics
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: -
Pages: 36 Volume / Issue: 56 (10) Sequence Number: 103512 Start / End Page: - Identifier: ISSN: 0022-2488
CoNE: /journals/resource/954922836227