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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.
 Noninterlacing 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.
 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.
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.
 An inverse spectral problem related to the Geng–Xue twocomponent peakon equation.
Hans Lundmark and Jacek Szmigielski.
Memoirs of the American Mathematical Society, Volume 244, Number 1155, 2016. viii+87 pages.
 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.
 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.
 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.)
Correction: At two places in Section 1, the factor m_{k} is missing on the righthand side of the ODE dm_{k}/dt = −(b1) 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.

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.
Corrections:
 In Corollary 4.17, C_{k}/A_{k} should be D_{k}/A_{k+1}.
 In Theorem 4.19, C_{k}D_{k} should be D_{k}^{2}.

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.
Corrections:
 In the proof of Proposition 2.3, −log(1−c) should be −log(1−√c).
 In equation (2.46), M_{2}z should be M_{2}z^{2}.
 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.)

Multipeakon 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
m_{3}(t) at the very end of published version of the article.

Higherdimensional 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.

Driven Newton equations and separable timedependent potentials.
Hans Lundmark and Stefan RauchWojciechowski.
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.
The thesis consists of an introduction plus three papers:
 Higherdimensional integrable Newton systems with
quadratic integrals of motion. (A revised version has been published; see above.)
 Driven Newton equations and separable timedependent potentials.
(A revised version has been published; see above.)
 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.

QuasiLagrangian systems of Newton equations.
Stefan RauchWojciechowski, 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.
 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.
 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.
 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.
 Dynamiska system.
25 min popular talk in Swedish, during "Populärvetenskapliga veckan" at Linköping University, Oct 24, 2012.
Recorded by Swedish national television.
 Ghostpeakons.
25 min talk given at the NEEDS 2012 (Nonlinear Evolution Equations and Dynamical Systems) conference in Kolymbari, Crete, July 14, 2012.
 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.
 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.
 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…)
 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.
 The Canada Day Theorem.
60 min colloquium talk given at the University of Saskatchewan, Saskatoon, Canada, September 4, 2009.
 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.
 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).
 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.