Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • Appendix D - Riemann #-functions and meromorphic forms

  • from Part III - Appendix
  • Eric D'Hoker, University of California, Los Angeles, Justin Kaidi, Kyushu University
  • Book:
    Modular Forms and String Theory
    Published online:
    28 November 2024
    Print publication:
    12 December 2024, pp 391-402

  • Summary

    In this final appendix, we shall review the modular geometry of the Siegel half-space at higher rank, Riemann theta-functions of higher rank, the embedding of higher-genus Riemann surfaces into the Jacobian variety via the Abel map, and use these ingredients to construct the prime form, the Szego kernel, and other meromorphic functions and differential forms on higher-genus Riemann surfaces.

  • PERIODIC PEAKONS AND CALOGERO–FRANÇOISE FLOWS

  • R. Beals, D. H. Sattinger, J. Szmigielski
  • Journal:
    Journal of the Institute of Mathematics of Jussieu / Volume 4 / Issue 1 / January 2005
    Published online by Cambridge University Press:
    10 February 2005, pp. 1-27
    Print publication:
    January 2005

  • It has long been known that a number of periodic completely integrable systems are associated to hyperelliptic curves, for which the Abel map linearizes the flow (at least in part). We show that this is true for a relatively recent such system: the periodic discrete reduction of the shallow water equation derived by Camassa and Holm. The associated spectral problem has the same form and evolves in the same way as the spectral problem for a family of finite-dimensional non-periodic Hamiltonian flows introduced by Calogero and Françoise. We adapt the Weyl function method used earlier by us to solve the peakon problem to give an explicit solution to both the periodic discrete Camassa–Holm system and the (non-periodic) Calogero–Françoise system in terms of theta functions.

    AMS 2000 Mathematics subject classification: Primary 35Q51; 37J35; 35Q53