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Hans Lundmark's publications and talks

Unpublished preprints

Nothing new right now.

Talks

• Peakons and shockpeakons in the Degasperis–Procesi equation.
  25 min talk given at the NEEDS 2007 workshop in l'Ametlla de Mar, Spain, June 19, 2007.
  • Presentation for fullscreen viewing (PDF file).
  • 4-up with white background for printing (PS file).
  
  
• Peakons and shockpeakons: an introduction to the world of nonsmooth solitons.
  60 min colloquium talk given in Paris (Séminaire de Géométrie Hamiltonienne, Institut de Mathématiques de Jussieu) on October 19, 2007 (and at various other places later).
  • Presentation for fullscreen viewing (PDF file).
  • 4-up with white background for printing (PS file).
    
  
  
• Explicit solutions of Novikov's peakon equation.
  40 min talk given at the XXVIII Workshop on Geometric Methods in Physics in Białowieża, Poland, July 4, 2009.
  • Presentation for fullscreen viewing (PDF file).
  • 4-up with white background for printing (PS file).
    
  
  
• The Canada Day Theorem.
  60 min colloquium talk given at the University of Saskatchewan, Saskatoon, Canada, September 4, 2009.
  • Presentation for fullscreen viewing (PDF file).
  
  
• Peakon equations related to the cubic string.
  35 min talk given at the GDIS 2010 (Geometry, Dynamics, Integrable Systems) conference in Fruška Gora near Belgrade, Serbia, September 12, 2010. (In case you wonder why I've made the text so LARGE, it's because they had a very small screen in the lecture hall! As a consequence, this talk easily broke my previous personal record for the largest number of slides per minute…)
  • Presentation for fullscreen viewing (PDF file).
• Orthogonal and biorthogonal polynomials in the theory of peakon equations.
  20 min talk given at the Completely Integrable Systems and Applications conference in Vienna, Austria, July 7, 2011.
  • Presentation for fullscreen viewing (PDF file).

Publications (in reverse chronological order)

• Get the list of publications from MathSciNet or Scopus (subscription needed).


• Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa–Holm type equation.
  Andrew N. W. Hone, Hans Lundmark and Jacek Szmigielski.
  Dynamics of Partial Differential Equations, Volume 6, Number 3 (September 2009): 253–289. 37 pages.
  • Journal website (open access): Andrew Hone, Hans Lundmark and Jacek Szmigielski, DPDE 6(3) (Sept 2009): 253–289.
  • Preprint version: arXiv:0903.3663 [nlin.SI].
  
  
• Continuous and discontinuous piecewise linear solutions of the linearly forced inviscid Burgers equation.
  Hans Lundmark and Jacek Szmigielski.
  Journal of Nonlinear Mathematical Physics, Volume 15, Supplement 3 (October 2008): 264–276. 13 pages.
  (Proceedings of NEEDS 2007.)
  • Journal website (open access): Hans Lundmark and Jacek Szmigielski, JNMP 15, Suppl. 3 (Oct 2008): 264–276.
  • Preprint version: arXiv:0805.1258 [nlin.SI].
  
  
• Formation and dynamics of shock waves in the Degasperis–Procesi equation.
  Hans Lundmark.
  Journal of Nonlinear Science, Volume 17, Number 3 (June 2007): 169–198. 30 pages.
  • Journal website (subscription needed): Hans Lundmark, J. Nonlinear Sci. 17 (June 2007): 169–198.
  • Preprint version from Jan 30, 2006 (29 pages): download from here (PDF, PS) or from the preprint server at the Institut Mittag-Leffler.
  
  
• The inverse spectral problem for the discrete cubic string.
  Jennifer Kohlenberg, Hans Lundmark, and Jacek Szmigielski.
  Inverse Problems, 23 (February 2007): 99–121. 23 pages.
  • Journal website (subscription needed): Jennifer Kohlenberg, Hans Lundmark, and Jacek Szmigielski, Inv. Prob. 23 (Feb 2007): 99–121.
  • Preprint version at arxiv.org: math.SP/0611745.
  
  
• Degasperis–Procesi peakons and the discrete cubic string.
  Hans Lundmark and Jacek Szmigielski.
  International Mathematics Research Papers, Volume 2005, Issue 2, pp. 53–116. 64 pages.
  • Journal website (subscription needed): Hans Lundmark and Jacek Szmigielski, IMRP, Volume 2005, Issue 2, 2005.
  • Preprint version at arXiv.org (58 pages): nlin.SI/0503036.
  • I have lots of reprints! Contact me if you want one (or two, or ten…).
  
  
• Multi-peakon solutions of the Degasperis–Procesi equation.
  Hans Lundmark and Jacek Szmigielski.
  Inverse Problems, 19 (December 2003): 1241–1245. 5 pages.
  • Journal website (subscription needed): Hans Lundmark and Jacek Szmigielski, Inv. Prob. 19 (Dec 2003): 1241–1245.
  • Updated version at arXiv.org: nlin.SI/0503033. This version corrects a few minor errors; in particular, the denominators λ_i+λ_j should not be squared in the expression for m₃(t) at the very end of the article.
  
  
• Higher-dimensional integrable Newton systems with quadratic integrals of motion.
  Hans Lundmark.
  Studies in Applied Mathematics, 110(3):257–296. 40 pages.
  • Journal website (subscription needed): Hans Lundmark, Studies in Applied Mathematics, Volume 110, Issue 3, 257–296, April 2003.
  • I have a number of reprints. Email me if you want one.
  
  
• Driven Newton equations and separable time-dependent potentials.
  Hans Lundmark and Stefan Rauch-Wojciechowski.
  Journal of Mathematical Physics, 43(12):6166–6194 (2002). 29 pages.
  • Journal website (subscription needed): Hans Lundmark and Stefan Rauch-Wojciechowski, J. Math. Phys. 43(12):6166–6194, 2002.
  • Local copies: PDF, gzipped PS
    Copyright (2002) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
  
  
• Newton Systems of Cofactor Type in Euclidean and Riemannian Spaces.
  Hans Lundmark (PhD thesis, Linköping University, November 2001).
  • Download: PDF, gzipped PS, DVI.
  • BibTeX entry.
  The thesis consists of an introduction plus three papers:
  1. Higher-dimensional integrable Newton systems with quadratic integrals of motion. (A revised version has been published; see above.)
  2. Driven Newton equations and separable time-dependent potentials. (A revised version has been published; see above.)
  3. Multiplicative structure of cofactor pair systems in Riemannian spaces. (This is a nice little paper, much prettier than the one about driven equations for example. However, Franco Magri and I discovered a little later that it is a special case of some results that he and his coworkers had obtained around the same time, as part of a large and impressive work on "ωN manifolds". So I never bothered to publish this, but as far as I can tell, they haven't yet published their results either… My results have been generalized further by Jens Jonasson, another PhD student of Stefan Rauch.)
  Let me know if you want a printed version of the thesis. I have loads of them!
  
  
• A new class of integrable Newton systems.
  Hans Lundmark.
  Journal of Nonlinear Mathematical Physics, Volume 8, pp. 195–199, Supplement, February 2001.
  Proceedings of NEEDS '99, Kolymbari, Crete. 5 pages.
  • Journal website (open access): Proceedings of NEEDS '99. It is article number 34 in the list.
  • Local copies: PDF, gzipped PS
  
  
• Quasi-Lagrangian systems of Newton equations.
  Stefan Rauch-Wojciechowski, Krzysztof Marciniak, and Hans Lundmark.
  Journal of Mathematical Physics, 40(12):6366–6398, 1999. 33 pages.
  • Journal website (subscription needed): Stefan Rauch-Wojciechowski et al., J. Math. Phys. 40(12):6366–6398, 1999.
  • Local copies: PDF, gzipped PS
    Copyright (1999) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.