SECTION DE MATHEMATIQUES

Boris Buffoni
Senior Scientist

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Teaching activities

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Telephone: +41 (21) 693 49 87
E-mail: Boris.Buffoni@epfl.ch

Postal Address:
EPFL SB MATH PDE
MA C2 605 (Bâtiment 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 and E. Séré, Steady three-dimensional rotational flows: existence via Kato's approach to locally coercive problems, preprint, 2025. https://arxiv.org/pdf/2505.01748

B. Buffoni and J. F. Toland, Connected Sets in Global Bifurcation Theory, Springer, 2025. https://link.springer.com/book/9783031870507

B. Buffoni, M. Haragus, G. Iooss [2023], Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls, Journal of Differential Equations, 355, 193-218. https://authors.elsevier.com/sd/article/S0022039623000396

B. Buffoni, M.D. Groves, E. Wahlén [2022], Fully localised three-dimensional gravity-capillary solitary waves on water of infinite depth, Journal of Mathematical Fluid Mechanics , 24. https://doi.org/10.1007/s00021-022-00684-5

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: July 2023 © Boris Buffoni