SECTION DE MATHEMATIQUES

Boris Buffoni

Senior Scientist

Teaching activities

**Telephone**: +41 (21) 693 49 87

**Fax**: +41 (21) 693 43 03

**E-mail**: Boris.Buffoni@epfl.ch

**Postal Address**:

EPFL SB MATH PDE

MA C2 605 (Batiment MA)

Station 8

CH-1015 Lausanne
(Switzerland)

**Research interests**

- the Calculus of Variations applied to Lagrangian and Hamiltonian systems, optimal transportation in Lagrangian dynamics and hydrodynamics;
- semi-global minimisation methods for quasi-linear elliptic variational problems, the variational approach to capillary-gravity water waves and their energetic stability;
- local bifurcation and center-manifold theory for elliptic PDEs, the configurations of an infinite elastic cylinder under compression or traction;
- the analytic theory of global bifurcation, the existence in the large of gravity waves and their secondary bifurcations;
- the variational approach to homoclinic chaos, spatial chaos in capillary-gravity water waves and in vorticity dynamics;
- shooting methods for homoclinic solutions of ODE's;
- bifurcation theory for strongly indefinite nonlinear operators near boundary points of their essential spectrum.

** Publications and preprints**

B. Buffoni, E. Wahlén [2019],
Steady three-dimensional rotational flows: an approach via two stream functions and Nash-Moser iteration, *Analysis & PDE*,
**12-5**, 1225-1258. DOI 10.2140/apde.2019.12.1225

B. Buffoni, H. Schwetlick, J. Zimmer [2019],
Travelling heteroclinic waves in a Frenkel-Kontorova chain with anharmonic on-site potential, *Journal de Mathématiques Pures et Appliquées*, https://doi.org/10.1016/j.matpur.2019.01.002,
http://arxiv.org/pdf/1607.08534.pdf

B. Buffoni, M. D. Groves, E. Wahlén [2018],
A variational reduction and the existence of a fully-localised solitary wave for the three-dimensional water-wave problem with weak surface tension,
*Arch. for Rational Mech. and Analysis*, **228**, 773-820. Made available online by
Springer Nature Sharing,
see also
http://arxiv.org/pdf/1603.09189.pdf (old version).

B. Buffoni, H. Schwetlick, Johannes Zimmer [2017],
Travelling waves for a Frenkel-Kontorova chain, *Journal of Differential Equations*,
**263(4)**, 2317-2342.
https://authors.elsevier.com/a/1V2-h50j-Zsrk,
http://arxiv.org/pdf/1507.03189.pdf (old version)

B. Buffoni [2012],
Bifurcation analysis at a singular soliton state in fiber couplers,
*Advanced Nonlinear Studies*,
**12(4)**, 737-748.

B. Buffoni and G. R. Burton [2013], On the stability of travelling waves with
vorticity obtained by minimisation, *NoDEA Nonlinear Differential Equations Appl.*, **20(5)**, 1597-1629.
http://arxiv.org/pdf/1108.1890v1

B. Buffoni [2012],
Generalized Flows Satisfying Spatial Boundary Conditions,
*J. Math. Fluid Mech.*, **14**, 501-528.
The original publication is available in LINK at
http://link.springer.com/article/10.1007/s00021-011-0077-7

B. Buffoni, M. D. Groves, S. M. Sun and E. Wahlén [2013],
Existence and conditional energetic stability of three-dimensional
fully localised solitary-capillary water waves,
*Journal of Differential Equations*, ** 254(3)**, 1006-1096.
http://arxiv.org/pdf/1108.1890v1

B. Buffoni and L. Landry [2010],
Multiplicity of homoclinic orbits in quasi-linear
autonomous Lagrangian systems, *Discrete Contin. Dyn. Syst. - Series A*,
**27**, 75-116. The following file
paper.pdf is a pre-copy-editing,
author-produced PDF of an article accepted for publication in
*Discrete Contin. Dyn. Syst. - Series A* following peer review.
The definitive publisher-authenticated version is available online at
http://aimsciences.org/journals/displayArticles.jsp?paperID=4892"

B. Buffoni [2009],
Gravity solitary waves by minimization: an uncountable family,
*Topological Methods in Nonlinear Analysis*,
**34**, 339-352.

B. Buffoni, M. Esteban and E. Sere [2006],
Normalized Solutions to Strongly Indefinite Semilinear Equations,
*Advanced Nonlinear Studies*,
**6**, 323-347.

P. Bernard and B. Buffoni [2007], Weak KAM Pairs and Monge-Kantorovich Duality,
*Advanced Studies in Pure Mathematics*,
** 47-2**.

P. Bernard and B. Buffoni [2006], The Monge problem for supercritical Mane
potentials on compact manifolds,
*Advances in Mathematics*, **207**, 691-706.

P. Bernard and B. Buffoni [2007],
Optimal mass transportation and Mather theory,
*Journal of The European Mathematical Society*, **9**, 85-121.

B. Buffoni and S. Rey [2006],
Localized thickening of a compressed elastic band,
*Journal of Elasticity*,
**82**, 49-71.

B. Buffoni [2005],
Conditional energetic stability of gravity solitary waves in the presence
of weak surface tension,
*Topological Methods in Nonlinear Analysis*,
**25**, 41-68.

B. Buffoni [2004],
Existence by minimisation of solitary water waves on an ocean of
infinite depth,
*Ann. Inst. Henri Poincare-Analyse non
lineaire*,
**21 **, 503-516.

B. Buffoni [2004],
Existence and conditional energetic stability
of capillary-gravity solitary water waves by minimisation,
*Arch. Rat. Mech. Anal.*, ** 173 **, 25-68.
paper.pdf (copyright: Springer-Verlag)
The original publication is available in LINK at
http://link.springer.de

B. Buffoni, E. Sere and J.F. Toland [2005],
Minimization methods for quasi-linear problems,
with an application to periodic water waves,
*SIAM Journal on Math. Analysis*, **36**, 1080-1094.
paper.pdf

B. Buffoni, E. Sere and J.F. Toland [2003],
Surface water waves as saddle points of the energy,
*Calculus of Variations and Partial Diffential Equations *
**17 **,199-220.
Abstract.
The original publication is available in LINK at
http://link.springer.de

B. Buffoni and J.F. Toland [2001], Dual free boundaries for Stokes waves,
*C. R. Acad. Sci. Paris*, **332 (I)**, 73-78.
Abstract.

B. Buffoni [2002], A variational formulation of three-dimensional steady
water waves, * Phil. Trans. R. Soc. Lond. A*, ** 360**, 2111-2126.

B. Buffoni [2002], Homoclinic orbits for eventually autonomous
high-dimensional Hamiltonian systems,
*J. Math. Anal. Appl.*,
** 274**, 536-553.
Abstract.

B. Buffoni and A. Mielke [2001], On interfaces between incompatible
wells and elastic deformations of infinite cylinders,
*Calculus of Variations and Partial Differential Equations*,
** 13**, 469-489.
The original publication is available in LINK at
http://link.springer.de
See also paper.pdf (copyright: Springer-Verlag)

P. Bolle and B. Buffoni [1999], Multibump homoclinic solutions
to a centre equilibrium in a class of autonomous Hamiltonian systems,
*Nonlinearity*,** 12**, 1699-1716.

P.Bolle and B. Buffoni [2000],
Multiplicity of algebraically
decaying solitary waves,
in volume 2 of the *Proceedings of the International
Conference on Differential Equations (Berlin, Germany, 1-7 August 99)*,
B. Fiedler, K. Groeger and J. Sprekels Eds,
World Scientific Publishing, Singapore, pp 1339-1344.

B. Buffoni, E.N. Dancer and J.F. Toland [2000],
The Regularity and Local Bifurcation of Steady Periodic Water Waves,
*Arch. Rational Mech. Anal.*, ** 152**, 207-240.
The original publication is available in LINK at
http://link.springer.de

B. Buffoni, E.N. Dancer and J.F. Toland [2000], The Sub-Harmonic
Bifurcation of Stokes Waves,
*Arch. Rational Mech. Anal.*, ** 152**, 241-271.
The original publication is available in LINK at
http://link.springer.de

B. Buffoni, E. N. Dancer and J. F. Toland [1998], Sur les ondes de Stokes
et une conjecture de Levi-Civita, *C. R. Acad. Sci. Paris*,**
326 (I)**, 1265-1268.

B. Buffoni [1999], Shooting methods and topological transversality,
*Proc. Roy. Soc. Edinburgh*, **129A**, 1137-1155.

B. Buffoni and M.D. Groves [1999], A multiplicity result for
solitary-capillary waves in deep water via critical point theory,
*Arch. Rational Mech. Anal,* **146**, 183-220.
The original publication is available in LINK at
http://link.springer.de

B. Buffoni [1997], Nested axi-symmetric vortex rings,
*Annales de l'IHP: Analyse non lineaire*,
**14**(6), 787-797.

B. Buffoni [1995], Multiplicity of homoclinic orbits in
fourth-order conservative systems, in *Proceedings
of the Workshop on Variational and Local Methods in the Study of
Hamiltonian Systems*, A. Ambrosetti and G.F. Dell'Antonio Eds,
World Scientific Publishing, Singapore, pp 129-136.

B. Buffoni and E. Sere [1996], A global condition for quasi-random behavior
in a class of conservative systems, *Communications on
Pure and Applied Mathematics*, **49**, 285-305.

B. Buffoni, M. Groves and J. Toland [1996], A plethora of capillary-gravity
waves with near-critical Bond and Froude numbers,
*Philosophical Transactions of the Royal Society of
London*, **354A**, 575-607.

B. Buffoni and F. Giannoni [1995],
Brake periodic orbits of prescribed Hamiltonian for indefinite Lagrangian
systems,
*Discrete and Continuous Dynamical Systems*, **1**, 217-222.

A. Ambrosetti, D. Arcoya and B. Buffoni [1994],
Positive solutions for some semi-positone problems via bifurcation
theory, *Diff. Int. Equations*, **7**, 655-663.

B. Buffoni, A. R. Champneys and J.F. Toland [1996],
Bifurcation and coalescence of a plethora of homoclinic orbits
for a Hamiltonian system, *J. of Dyn. and Diff.
Eq.*, **8**, 221-279.

B. Buffoni [1996],
Periodic and homoclinic orbits for Lorentz-Lagrangian systems
via variational methods, *Nonlinear Analysis TMA*, **26**, 443-462.

B. Buffoni [1995],
Infinitely many large amplitude homoclinic orbits for a class
of autonomous Hamiltonian systems,
*J. of Diff. Eq.*, **121**, 109-120.

B. Buffoni and J.F. Toland [1995],
Global bifurcation of homoclinic and periodic
orbits for autonomous Hamiltonian systems,
*J. of Diff. Eq*, **118**, 104-120.

B. Buffoni [1993], Cascade of homoclinic orbits for Hamiltonian systems:
further properties, *Nonlinearity*, **6**, 1091-1092.

B. Buffoni [1992], Un probleme variationnel fortement indefini sans compacite, PhD thesis, Ecole Poly. Fed. de Lausanne.

B. Buffoni, L. Jeanjean and C.A. Stuart [1993], Existence of a
non-trivial solution to
a strongly indefinite semilinear equation,
*Proceedings of the A.M.S.*,
**119**(1), 179-186.

B. Buffoni and L. Jeanjean [1993], Minimax characterization of solutions for a
semi-linear elliptic equation, *Ann. Inst. Henri Poincare-Analyse non
lineaire*,
**10**(4), 377-404.

B. Buffoni and L. Jeanjean [1993],
Bifurcation from the spectrum towards regular
values,
*J. reine angew. Math.*, **445**, 1-29.

B. Buffoni [1990], Discrete spectrum of perturbed Dirac systems with real and
periodic coefficients, *Proc. Roy. Soc. Edinburgh*, **115A**, 337-347.

** Books**

B.Buffoni and J. F. Toland,
*Introduction à la Théorie Globale des Bifurcations*,
Presses Polytechniques et Universitaires Romandes, 2002.

B.Buffoni and J. F. Toland,
*Analytic Theory of Global Bifurcation*,
Princeton
University Press, 2003.

**Summary** of the output of a research funded by EPSRC at
the Department of Mathematical Sciences of the University of Bath from December 1997
to August 1998:
EPSRC grant GR/L41059

Last update: *June 2017*
© *Boris Buffoni*