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Hans Lundmark's publications and talks

Current preprints

Nothing new right now.

Works in progress

• Peakon–antipeakon solutions of the Novikov equation.
  Marcus Kardell and Hans Lundmark.
  A preliminary version was included as Paper II in Marcus's PhD thesis, defended Feb 2016 (pdf file including Papers I and II, record in the DiVA database). Our conjecture in Remark 5.5 that the eigenvalues must lie in the open right half plane turned out to be false, so the results in this preliminary version are incomplete since they don't cover the case when there are eigenvalues on the imaginary axis. Other duties have made it difficult to find time for working on the final version, but we're still hoping to finish this paper some day…
• Projective dynamics and cofactor systems.
  Alain Albouy and Hans Lundmark.
  Still in the early stages of writing.

Publications (in reverse chronological order)

• Get the list of publications from MathSciNet or Scopus (subscription needed), or from ORCID (free).
• Or the list of my preprints on arXiv.


• A view of the peakon world through the lens of approximation theory.
  Hans Lundmark and Jacek Szmigielski.
  Physica D: Nonlinear Phenomena, Volume 440, November 2022, article 133446. 44 pages.
  • Journal website (open access): Physica D 440 (2022), 133446.
  • Preprint version (July 2022, 58 pages): arXiv:2203.12954 [nlin.SI].
  
  
• Non-interlacing peakon solutions of the Geng–Xue equation.
  Budor Shuaib and Hans Lundmark.
  Journal of Integrable Systems, Volume 4, Issue 1, 2019, article xyz007. 115 pages.
  • Journal website (open access): J. Integrable Syst. 4(1) (2019), xyz007.
  • Preprint version (December 2018, 133 pages): arXiv:1812.09173 [math-ph].
  
  
• Ghostpeakons and characteristic curves for the Camassa–Holm, Degasperi–Procesi and Novikov equations.
  Hans Lundmark and Budor Shuaib.
  SIGMA, Volume 15, 2019, article 017. 51 pages.
  • Journal website (open access): SIGMA 15 (2019), 017.
  • The same version is also available from arXiv.org: arXiv:1807.01910 [nlin.SI].
  Corrections:
  • Unnumbered equation above (2.9): Sign error in u_x(x_k), remove the minus sign in front of the sum.
  
  
• Dynamics of interlacing peakons (and shockpeakons) in the Geng–Xue equation.
  Hans Lundmark and Jacek Szmigielski.
  Journal of Integrable Systems, Volume 2, Issue 1, 2017, article xyw014. 65 pages.
  • Journal website (open access): J. Integrable Syst. 2(1) (2017), xyw014.
  • Preprint version (May 2016, 59 pages): arXiv:1605.02805 [nlin.SI].
  
  
• An inverse spectral problem related to the Geng–Xue two-component peakon equation.
  Hans Lundmark and Jacek Szmigielski.
  Memoirs of the American Mathematical Society, Volume 244, Number 1155, 2016. viii+87 pages.
  • Journal website (subscription needed): Mem. Amer. Math. Soc., 244(1155) (2016).
  • Preprint version (April 2013, 78 pages): arXiv:1304.0854 [math.SP].
  
  
• The Canada Day Theorem.
  Daniel Gomez, Hans Lundmark and Jacek Szmigielski.
  The Electronic Journal of Combinatorics, Volume 20, Issue 1, 2013, article id #P20. 16 pages.
  • Journal website (open access): Electron. J. Combin., 20(1) (2013), #P20.
  • Preprint version (June 2012): arXiv:1206.4138 [math.CO].
  
  
• 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, pp. 253–289. 37 pages.
  • Journal website (open access): DPDE 6(3) (Sept 2009): 253–289.
  • Preprint version (March 2009): 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, pp. 264–276. 13 pages.
  (Proceedings of NEEDS 2007.)
  • Journal website (open access): JNMP 15, Suppl. 3 (Oct 2008): 264–276.
  • Preprint version (May 2008): arXiv:0805.1258 [nlin.SI].
  Correction: At two places in Section 1, the factor m_k is missing on the right-hand side of the ODE dm_k/dt = −(b-1) m_k u_x(x_k).
  
  
• Formation and dynamics of shock waves in the Degasperis–Procesi equation.
  Hans Lundmark.
  Journal of Nonlinear Science, Volume 17, Issue 3, June 2007, pp. 169–198. 30 pages.
  • Journal website (subscription needed): J. Nonlinear Sci. 17 (June 2007): 169–198.
  • Preprint version (Jan 2006, 29 pages): Download from here (PDF, PS), or via Dissemin. It used to be at the preprint server of the Institut Mittag-Leffler, but was removed when their website was reorganized; however, courtesy of the Internet Archive Wayback Machine, here's an archived version of that page.
  
  
• The inverse spectral problem for the discrete cubic string.
  Jennifer Kohlenberg, Hans Lundmark, and Jacek Szmigielski.
  Inverse Problems, Volume 23, Number 1, February 2007, pp. 99–121. 23 pages.
  • Journal website (subscription needed): Inv. Prob. 23 (Feb 2007): 99–121.
  • Preprint version (Nov 2006): arXiv:math/0611745 [math.SP].
  Corrections:
  • In Corollary 4.17, C_k/A_k should be D_k/A_k+1.
  • In Theorem 4.19, C_kD_k should be D_k².
  
  
• Degasperis–Procesi peakons and the discrete cubic string.
  Hans Lundmark and Jacek Szmigielski.
  International Mathematics Research Papers, Volume 2005, Issue 2, 2005, pp. 53–116. 64 pages.
  • Journal website (subscription needed): IMRP, Volume 2005, Issue 2, 2005.
  • Preprint version (March 2005, 58 pages): arxiv:nlin.SI/0503036.
  • I have lots of reprints! Contact me if you want one (or two, or ten…).
  Corrections:
  • In the proof of Proposition 2.3, −log(1−c) should be −log(1−√c).
  • In equation (2.46), M₂z should be M₂z².
  • In equation (A.3), −zg_k should be zg_k.
  • In reference [12], F. P. Gantmacher should be F. R. Gantmacher. (This error comes from MathSciNet's database.)
  
  
• Multi-peakon solutions of the Degasperis–Procesi equation.
  Hans Lundmark and Jacek Szmigielski.
  Inverse Problems, Volume 19, Number 6, December 2003, pp. 1241–1245. 5 pages.
  • Journal website (subscription needed): Inv. Prob. 19 (Dec 2003): 1241–1245.
  • Updated version: arxiv: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 published version of the article.
  
  
• Higher-dimensional integrable Newton systems with quadratic integrals of motion.
  Hans Lundmark.
  Studies in Applied Mathematics, Volume 110, Issue 3, April 2003, pp. 257–296. 40 pages.
  • Journal website (subscription needed): Studies in Applied Mathematics, Volume 110, Issue 3, 257–296, April 2003.
  • Self-archived peer reviewed version (identical to the published one except for formatting): PDF.
  • 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, Volume 43, Issue 12, 2002, pp. 6166–6194. 29 pages.
  • Journal website (subscription needed): 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, Supplement (Proceedings of NEEDS '99, Kolymbari, Crete), February 2001, pp. 195–199.
  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, Volume 40, Issue 12, 1999, pp. 6366–6398. 33 pages.
  • Journal website (subscription needed): 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.

Talks (in reverse chronological order)

• Dynamics of peakons and antipeakons in Novikov's equation.
  50 min talk given at the 2024 CMS Summer Meeting (session CH – thirty years later) at the University of Saskatchewan, Saskatoon, Canada, June 1, 2024.
  • Presentation for fullscreen viewing (PDF file).
• Peakons in pictures.
  60 min talk given in connection with the conference Flows on the Saskatchewan: A Workshop on Integrability and Inverse Problems at the University of Saskatchewan, Saskatoon, Canada, April 8, 2019.
  • Presentation for fullscreen viewing (PDF file).
• Peakon solutions of the Novikov and Geng–Xue equations.
  50 min talk given at the conference Nonlinear Phenomena in Stockholm: Kinetic Meets Dispersive at KTH, Stockhom, Sweden, Nov 21, 2018.
  • Presentation for fullscreen viewing (PDF file).
• Some recent advances in the study of peakons.
  25 min talk given at the 27th Nordic Congress of Mathematicians (session Nonlinear PDEs: boundary value problems and equations arising in fluid mechanics) in Stockhom, Sweden, March 17, 2016.
  • Presentation for fullscreen viewing (PDF file).
• Dynamiska system.
  25 min popular talk in Swedish, during "Populärvetenskapliga veckan" at Linköping University, Oct 24, 2012. Recorded by Swedish national television.
  • Video (FLV file, 181 MB).
  • Slides (PDF file).
• Ghostpeakons.
  25 min talk given at the NEEDS 2012 (Nonlinear Evolution Equations and Dynamical Systems) conference in Kolymbari, Crete, July 14, 2012.
  • Presentation for fullscreen viewing (PDF file).
• Peaked solitons.
  25 min talk given at the Satellite Thematic Session: Integrable Systems of the 6th European Congress of Mathematics in Kraków, Poland, July 2, 2012.
  • 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).
• 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).
• From water waves to combinatorics: The mathematics of peaked solitons.
  My docent lecture given here at the math department in Linköping on April 26, 2010.
  • Presentation for fullscreen viewing (PDF 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).
• 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).
    
• 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).
    
• 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).