Panayiotis G. Panayotaros Departamento de Matemáticas y ...

Panayiotis G. Panayotaros
Departamento de Matemáticas y Mecánica
I.I.M.A.S., Universidad Nacional Autónoma de México
Apartado Postal 20-726, 01000 México, D.F.
Office (55) 5622-3600, Fax (55) 5622-3564
panos@mym.iimas.unam.mx
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EDUCATION
• Ph.D., Physics, University of Texas at Austin, 1997.
Advisor: R. de la Llave.
• M.A., Physics, University of Texas at Austin, 1992.
• B.S., Mathematics, University of Chicago, 1990.
PROFESSIONAL EXPERIENCE
• Investigador Titular A Interino, Departamento de Matemáticas y Mecánica, Instituto
de Investigaciones en Matemáticas Aplicadas y en Sistemas (I.I.M.A.S.),
Universidad Nacional Autónoma de México (U.N.A.M.), México D.F., México,
Mayo 2007 - Present.
• Investigador Asociado C, Departamento de Matemáticas y Mecánica, Instituto de
Investigaciones en Matemáticas Aplicadas y en Sistemas (I.I.M.A.S.), Universidad
Nacional Autónoma de México (U.N.A.M.), México D.F., México, October 2003 -
May 2007.
• NSF VIGRE Postdoctoral Research Associate, Department of Appliead Mathematics
University of Colorado at Boulder,U.S.A., September 2000-June 2003.
• Investigador Asociado C, Departamento de Matemáticas y Mecánica, Instituto de
Investigaciones en Matemáticas Aplicadas y en Sistemas (I.I.M.A.S.), Universidad
Nacional Autónoma de México (U.N.A.M.), México D.F., México, February 1998
- August 2000.
RESEARCH INTERESTS
• Nonlinear dispersive waves: Hamiltonian methods, nonlinear stability;
• Nonlinear optics: dispersion and diffraction management, nonlinear lattices;
• Fluid mechanics: water waves; Elasticity: surface waves;
• Hamiltoniana dynamics: local and perturbation methods, variational methods.
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PUBLICATIONS
• P. Panayotaros, D.E. Pelinovsky: Periodic oscillations of discrete NLS solitons in
the presence of diffraction management, Nonlinearity 21 1265-1279 (2008)
• P. Panayotaros: Invariant tori in the discrete NLS with small amplitude diffraction
management, Physica D 37, 829-839 (2008)
• P. Panayotaros: Multibreather solitons in the diffraction managed NLS equation ,
Phys. Let. A, Phys. Let. A 349, 430-438 (2006).
• P. Panayotaros: Breather solutions in the diffraction managed NLS equation, Physica
D 206, 213-231 (2005).
• P. Panayotaros: Averaging and Benjamin-Feir instabilities in a parametrically
forced nonlinear Schrödinger equation, Phys. Lett. A 323, 403-414 (2004).
• P. Panayotaros: Quartic normal forms for the periodic dispersion managed nonlinear
Schrödinger equation, Physica D 191, 219-237 (2004).
• P. Panayotaros: An expansion method for non-linear Rayleigh waves, Wave Motion
36, 1-21 (2002).
• P. Panayotaros: Amplitude equations for non-linear Rayleigh waves , Phys. Lett.
A 289, 111-120 (2001).
• P. Panayotaros: Near-monochromatic water waves on the sphere, Physica D 130,
273-290 (1999).
• P. Panayotaros: Diagrams in classical and semi-classical perturbation theory, J.
Math. Phys. 39, 4, 1997-2003 (1998).
• R. de la Llave, P. Panayotaros: Water waves on the surface of the sphere, J. Nonlin.
Sci. 6, 147-167 (1996).
• P. Panayotaros: Traveling surface elastic waves in the half-plane, Proc. A.M.S.-
I.M.S.-S.I.A.M. Conf. on Dispersive wave turbulence, Contemp. Math. 283, 83-90
(2001).
• P. Panayotaros: Stability of traveling water waves on the sphere, Proc. of 1999
I.M.A.C.S. Conf. on Nonlinear waves, Math. Com. Sim. 55, 577-584 (2001).
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• P. Panayotaros: Traveling water waves on the sphere, Proc. of 1998 E.P.S.-A.P.S.-
I.U.P.A.P. Conf. on Comp. Phys., Comp. Phys. Com. 121-122, 386-387 (1999).
Accepted Articles
• L.A. Cisneros, A.M. Minzoni, P. Panayotaros, N.F. Smyth: Modulation analysis
of large scale discrete vortices, to appear in Physical Review E.
Other articles
• P. Panayotaros: Linear stability of real breathers in the discrete NLS, preprint
(2008).
• P. Panayotaros, M. Sepúlveda, O. Vera: Standing waves for the dispersion management
of a coupled nonlinear Schrödinger system, preprint (2008).
• P. Panayotaros: Continuation of breathers in the discrete NLS with rapid parametric
forcing, preprint (2007).
• P. Panayotaros: Minimal Jacobi geodesics in the planar n-center problem, preprint,
available at http://www.fenomec.unam.mx/publicaciones/articulos.html (2002).
• P. Panayotaros: Nekhoroshev stability of non-linear normal modes near an elliptic
fixed point of a Hamiltonian system with symmetry, preprint,
available http://www.ma.utexas.edu/mp arc/papers/99-62.
• P. Panayotaros: Numerical simulation of surface water waves on the sphere, preprint,
available at http://www.ma.utexas.edu/mp arc/papers/97-460.
• P. Panayotaros: Gravity waves on the surface of the sphere, Ph.D. Thesis, University
of Texas at Austin, 1997.
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CONFERENCE TALKS
• Stability of breathers in the discrete NLS, S.I.A.M. Conf. on Nonlinear Waves and
Coherent Structures, Rome, Italy, 2008.
• Breather solutions in the discrete NLS with parametric forcing, A.M.S.-A.M.A.
Annual Joint Meeting, San Diego, California, U.S.A., 2008.
• Continuation of breathers in the discrete NLS with parametric forcing, C.R.M.S.
Workshop on Hamiltonian Advace-Delay Equations, Halifax, Canada, 2007.
• Breathers in the discrete NLS with diffraction management, S.M.M.-A.M.S. Joint
Meeting, Zacatecas, México, 2007.
• Breathers in the discrete NLS with diffraction management, C.I.C. Gathering on
Nonlinear Lattice Dynamics, Cuernavaca, México, 2007.
• Invariant tori in the discrete NLS with diffraction management, C.M.S.-S.M.M.
Joint Meeting, Guanajuato, México, 2006.
• Invariant tori in the discrete NLS with diffraction management, S.I.A.M. Conf. on
Nonlinear Waves and Coherent Structures, Seattle, Washington, U.S.A., 2006.
• Invariant tori in the discrete NLS with diffraction management, Panhellenic Conf.
on Nonlinear Science and Complexity, Thessaloniki, Greece, 2006.
• Breathers and multibreathers in some discrete NLS equations, S.M.M. Annual
Meeting, México D.F., México, 2006.
• Multibreathers in the diffraction managed discrete NLS, poster presentation, Dynamics
Days Europe, Berlin, Germany, 2005.
• Breather solitons in some discrete NLS equations, Panamerican Adv. Studies Institute
on Differential Equations, Santiago, Chile, 2005.
• Breather solitons in some discrete NLS equations, S.I.A.M. Conf. on Nonlinear
Waves and Coherent Structures, Orlando, Florida, U.S.A., 2004.
• Averaging and solitons in the dispersion managed NLS equation, A.M.S.-S.M.M.
Joint Meeting, Houston, Texas, U.S.A, 2004.
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• Birkhoff normal forms for the periodic DMNLS equation, I.M.A.C.S. Int. Conf. on
Nonlinear Evolution Equations and Wave Phenomena, Athens, Georgia, U.S.A.,
2003.
• Jacobi minimizers in the planar n-center problem, Americas Conf. on Differential
Equations, Edmonton, Canada, 2002.
• Jacobi minimizers in the planar n-center problem, Variational Methods: Open
Problems, Recent Progress, and Numerical Algorithms, Flagstaff, Arizona, U.S.A.,
2002.
• Nonlinear Rayleigh waves, C.M.I. Symposium and Euro Workshop on Hamiltonian
Systems, Edinburgh, U.K., 2001.
• Singularity formation in nonlinear Rayleigh waves, A.M.S.-S.M.M. Joint Meeting,
Morelia, México, 2001.
• Singularity formation in nonlinear Rayleigh waves, Arkansas Spring Lecture Series:
P.D.E. in Periodic Media, Fayetteville, Arkansas, U.S.A., 2001.
• Surface elastic waves of permanent form, I.M.A.C.S. Int. Conf. on Nonlinear
Evolution Equations and Wave Phenomena, Athens, Georgia, U.S.A., 2001.
• Nonlinear Rayleigh waves, Southwest Dynamical Systems Conf., Los Angeles,
California, U.S.A., 2000.
• Traveling surface elastic waves in the half-plane, A.M.S.-I.M.S.-S.I.A.M. Workshop
on Weak Turbulence, Mount Holyoke, Massachusetts, U.S.A., 2000.
• Ondas elasticas de superficie nolineales, S.M.M. Annual Meeting, Guadalajara,
México, 1999.
• Water waves on the sphere, I.C.M.S. Workshop on Hamiltonian Mechanics and
Small Divisors in P.D.E., Edinburgh, U.K., 1999.
• Stability of water waves on the sphere, I.M.A.C.S. Int. Conf. on Nonlinear Evolution
Equations and Wave Phenomena, Athens, Georgia, U.S.A., 1999.
• Near-monochromatic water waves on the sphere, E.P.S.-A.P.S.-I.U.P.A.P.
Conference on Computational Physics, Granada, Spain, 1998.
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• Gravity water waves on the sphere, Midwest-Southeastern-Atlantic Joint Regional
Conference on Differential Equations, Nashville, Tennessee, U.S.A., 1997.
• Numerical simulation of gravity water waves on the sphere, N.A.S.A. Summer
School for High Performance Computational Fluid Dynamics, Washington D.C.,
U.S.A., 1997.
• Gravity water waves on the sphere, Texas P.D.E. Conference, Denton, Texas,
U.S.A., 1997.
• Gravity water waves on the sphere, Southwest Dynamical Systems Conf., Denton,
Texas, U.S.A., 1997.
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STUDENTS
• B.S. Thesis Advisor of Erick Yasser Martínez Serrano, Faculty of Science. Title:
Predator-prey model with Hopf bifurcation, defended October 2006.
• Co-advisor of Social Service of students Rebeca Cecilia de Buen Kalman, Faculty of
Science, and Serena Pérez Zanco, Faculty of Science, on generation and interaction
of solitons in a water wave channel, with M.C. Jorge, I.I.M.A.S.-U.N.A.M., and R.
Silva, Instituto de Ingeniería-U.N.A.M., project concluded in October 2006.
• Co-advisor of Social Service of José Alberto Morales, Faculty of Science, with
M.C. Jorge, I.I.M.A.S.-U.N.A.M., and R. Silva, Instituto de Ingeniería-U.N.A.M.,
project concluded in August 2007.
• B.S. Thesis Advisor of osé Alberto Morales Escalante, Faculty of Science, with
M.C. Jorge, I.I.M.A.S.-U.N.A.M. Title: Theory and experiments in solitary waves,
defended August 2007.
• Adisor of Master’s mini-thesis of Pedro Aceves Sanchez, Graduate Program in
Mathematical Sciences, in progress.
• Adisor of Master’s mini-thesis of Francisco Javier Martinez Farias, Graduate Program
in Mathematical Sciences, in progress.
• Co-advisor of Master’s mini-thesis of Sergio Alejandro de la Torre Perez, with M.C.
Jorge, I.I.M.A.S.-U.N.A.M., in progress.
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TEACHING EXPERIENCE
• 1999-I, P.D.E. I, undergrad, U.N.A.M.,
• 2000-I, Complex Variables I, undregrad, U.N.A.M.,
• 2000-II, Matrix Methods, undergrad, Univ. de Colorado en Boulder,
• 2001-I, Calculus I, undergrad, Univ. de Colorado en Boulder,
• 2001-II, Matrix Methods, undergrad, Univ. de Colorado en Boulder,
• 2002-I, Calculus I, undergrad, Univ. de Colorado en Boulder,
• 2002-II, Matrix Methods, undergrad, Univ. de Colorado en Boulder,
• 2003-I, Complex Variables, undergrad/graduate, Univ. de Colorado en Boulder,
• 2004-I, Introduction to Analytical Mechanics, graduate, U.N.A.M.,
• 2004-II, P.D.E. I, undergrad, U.N.A.M.,
• 2005-I, Complex Variables I, undergrad, U.N.A.M.,
• 2005-II, Introduction to Continuous Media, graduate, U.N.A.M.,
• 2006-I, Complex Variables I, undergrad, U.N.A.M.,
• 2006-II, P.D.E. I, undergrad, U.N.A.M.,
• 2007-I, Introduction to Analytical Mechanics, graduate, U.N.A.M.,
• 2007-II, Introduction to Continuous Media, graduate, U.N.A.M.,
• 2008-I, Numerical Methods in P.D.E.: Introduction to Spectral Methods, with
M.C. Jorge, graduate, U.N.A.M.,
• 2008-II, P.D.E. I, undergrad, U.N.A.M.,
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OTHER ACADEMIC ACTIVITIES AND SERVICE
• Co-organizer with V. Rothos, U. Thessaloniki, Greece, minisymposium on “Coherent
Structures in Nonlinear Lattices”, S.I.A.M. Conf. on Nonlinear Waves and
Coherent Structures, Rome, Italy, July 2008.
• Organizer with A. Bountis, U. Patras, Greece, A Minzoni, U.N.A.M., of workshop
“Nonlinear Waves in Continuous and Discrete systems” I.I.M.A.S.-U.N.A.M.,
México D.F., January 2008.
• Organizer with A. Bountis, U. Patras, Greece, A Minzoni, U.N.A.M., J. Fujioka,
U.N.A.M., C. Jung, U.N.A.M., of “Gathering on Nonlinear Lattice Dynamics:
from Localization to Statistical Behavior”, Centro Internacional de Ciencias, I.C.F
- U.N.A.M., Cuernavaca, January 2007.
• Organizer with J.D. Meiss, U. Colorado, Boulder, R. Easton, U. Colorado, Boulder,
of Fall 2001 Midwest Dynamical Systems Conference, Boulder, Colorado, October
2001.
• Member, Committee on P.D.E. Preliminary Exam, Departament of Applied Mathematics,
University of Colorado at Boulder, 2001-2002.
• Member, Continuous Media and Mechanics Preliminary Exam, Graduate Program
in Mathematical Sciences, U.N.A.M., 2004-Present.
• Ph.D. Thesis Committee Member, Luis Alberto Cisneros Ake, Graduate Program
in Mathematical Sciences, U.N.A.M. (2007).
• B.S. Thesis Committee Member for Abraham de la Rosa, Faculty of Science,
U.N.A.M. (2005), and Erika Fabiola Fernández Gómora, Faculty of Science, U.N.A.M.
(2006).
• M.A. Thesis Committee Member, Luis Miguel de la Cruz Salas, Graduate Program
in Computer Sciences, U.N.A.M. (1999).
• Principal Investigator, SEP-Conacyt 50303 “Ondas dispersivas nolineales y problemas
en cadenas”, with A. Minzoni, L.A. Cisneros Ake (2006-present).
• Sistéma Nacional de Investigadores, Nivel I, 2004-Present.
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