Welcome to the Miguel A. Alejo's home page.
There is not much here at the moment, but do not hesitate to contact me if you do not find what you are looking for.
Nowadays, I am Associate Professor at
Universidad de Córdoba (Dpto. de Matemáticas)
Edificio Einstein
Escuela Politécnica Superior de Córdoba
Campus de Rabanales, Córdoba, España
Office: sala 114
Ph.: (34) 957 21 1051
Fax: (34)
Research Interests: Nonlinear Partial Differential Equations, in particular: stability of coherent states, integrability. Mathematical Biology.
CV Lattes: http://lattes.cnpq.br/5546115588679639
Publications
30-M.A. Alejo and A.J. Corcho, Orbital stability of the black soliton for the quintic Gross-Pitaevskii equation, Rev. Mat. Iberoam. (2024), published online first, doi: 10.4171/RMI/1467; arXiv:2003.09994
29-M.A. Alejo, Higher order mKdV breathers: nonlinear stability, Proyecciones (Antofagasta, On line), vol. 43, no. 2, pp. 495-520, Apr. 2024. doi.org/10.22199/issn.0717-6279-6048
28-M.A. Alejo, C. Muñoz and J.M. Palacios, On the asymptotic stability of the sine-Gordon kink in the energy space, Comm. Math. Physics (2023), Comm.Math.Phys.2023, arXiv:2003.09358
27-M.A. Alejo, M. Cavalcante and A.J. Corcho, Stability of mKdV breathers on the half-line, Partial Differ. Equ. Appl. 3, 70 (2022). https://doi.org/10.1007/s42985-022-00209-9, arXiv:2206.02898v1
26-M.A. Alejo, Dynamics of breathers in the Gardner hierarchy: universality of the variational characterization, Proyecciones (Antofagasta, On line), vol. 42, no. 4, pp. 833-860, Jul. 2023. doi.org/10.22199/issn.0717-6279-5354, arXiv:1901.10409
25-H. Kalisch, M.A. Alejo, D. Pilod and A.J. Corcho, Breather Solutions to the Cubic Whitham Equation, submitted, arXiv:2201.12074v1
24-M.A. Alejo and C. Maulén, Decay for Skyrme wave maps, Letters in Mathematical Physics, 112, 90 (2022). https://doi.org/10.1007/s11005-022-01585-4, arXiv:2108.01163
23-M.A. Alejo and J.L. López, Modeling chemotaxis with nonstandard production/degradation mechanisms from Doebner-Goldin theory: existence of solitary waves, Physica D: Nonlinear Phenomena, 426, 132989 (2021).
22-M.A. Alejo and C. Kwak, Global solutions and stability properties of the 5th order Gardner equation, Journal of Dynamics and Differential Equations, 35, 575-621, (2023). https://doi.org/10.1007/s10884-021-10022-4 arXiv:1901.03350
21-M.A. Alejo, L. Fanelli and C. Muñoz, Stability and instability of breathers in the U(1) Sasa-Satsuma and Nonlinear Schrödinger models, Nonlinearity, 34 (2021) 3429-3484, DOI: doi.org/10.1088/1361-6544/abea6c, arXiv:1901.10381
20-M.A. Alejo, L. Fanelli and C. Muñoz, Review on the stability of the Peregrine and related breathers, Frontiers in Physics, section Mathematical and Statistical Physics, (Mini-Review, Front. Phys., 24 (2020)) arxiv:2008.11590.
19-M.A. Alejo, Propagação de Pacotes de ondas: Breathers, (in portuguese) Rev. Matem. Universitária (RMU) n.1 2020
18-M.A. Alejo and J.L. López, On global solutions to some non-Markovian quantum kinetic models of Fokker-Planck type, ZAMP (Zeitschrift für Angewandte Mathematik und Physik), Z. Angew. Math. Phys. 71, 72 (2020). https://doi.org/10.1007/s00033-020-01295-8, arXiv:1811.12460
17-M.A. Alejo, L. Fanelli, and C. Muñoz, The Akhmediev Breather is unstable, SPJM (Proceed. Third Workshop on Nonlinear Dispersive Equations 2017 (Campinas, Brazil)), p. 1-11, http://link.springer.com/article/10.1007/s40863-019-00145-4, arXiv:1810.12543
16-M.A. Alejo, M. Cortez, C. Kwak, and C. Muñoz, On the dynamics of zero-speed solutions for Camassa-Holm type equations, IMRN (International Mathematics Research Notices), Vol. 2021, No. 9, pg. 6543–6585, DOI: 10.1093/imrn/rnz038, arxiv: 1810.09594
15-M.A. Alejo and E. Cardoso, On the ill-posedness of the 5th-order Gardner equation, SPJM 13, pg. 383-390 (2019), DOI: 10.1007/s40863-019-00150-7 arXiv:1810.10434
14-M.A. Alejo and C. Muñoz, Almost sharp nonlinear scattering in one-dimensional Born-Infeld equations arising in nonlinear Electrodynamics. Proceedings of the AMS, Vol.146, Num. 5, May 2018, pp. 2225–2237, http://www.ams.org/journals/proc/0000-000-00/S0002-9939-2018
13-M.A. Alejo, Nonlinear stability of Gardner breathers. Journal of Differential Equations Vol. 264/2, (2018) pp. 1192-1230. arxiv: 1705.04206 https://authors.elsevier.com/a/1W0w0_W4cMoNO
12-M.A. Alejo, C. Muñoz and J.M. Palacios, On the variational structure of breather solutions II: periodic mKdV equation, Electron. J. Differential Equations, Vol. 2017 (2017), No. 56, pp. 1-26. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu/Volumes/2017/56/alejo.pdf or http://ejde.math.unt.edu
11-M.A. Alejo, C. Muñoz and J.M. Palacios, On the variational structure of breather solutions I: sine-Gordon equation. Journal of Mathematical Analysis and Applications Vol.453/2 (2017) pp. 1111-1138. DOI 10.1016/j.jmaa.2017.04.056, http://www.sciencedirect.com/science/article/pii/S0022247X17304195
10-M.A. Alejo and C. Muñoz, Dynamics of complex-valued modified KdV solitons with applications to the stability of breathers. Analysis & PDE 8-3 (2015) 629--674. DOI 10.2140/apde.2015.8.629
9-B. Sánchez-Rey, N.R. Quintero, J. Cuevas-Maraver and M.A. Alejo, Collective Coordinates Theory for Discrete Soliton Ratchets in the sine-Gordon model. Phys. Rev. E 90 (2014), 042922, https://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042922; doi.org/10.1103/PhysRevE.90.042922
8-M.A. Alejo and C. Muñoz, Nonlinear stability of mKdV breathers. Communications in Mathematical Physics, \textbf{324}, 1, (2013), 233--262. http://link.springer.com/article/10.1007/s00220-013-1792-0
7-M.A. Alejo, C.Gorria and L.Vega, Discrete conservation laws and the convergence of long time simulations of the mKdV equation. J. Computational Phys. 235 (2013) 274--285. DOI: 10.1016/j.jcp.2012.10.044
6-M.A. Alejo, C. Muñoz and L. Vega, The Gardner equation and the $L^2$-stability of the N-Soliton solution of the Korteweg-de Vries equation. Transactions of the American Mathematical Society vol. 365 (2013), no. 1, 195–212.
http://www.ams.org/journals/tran/0000-000-00/S0002-9947-2012-05548-6/S0002-9947-2012-05548-6.pdf
5-M.A. Alejo and C. Muñoz, On the nonlinear stability of mKdV breathers. J. Phys. A: Math. Theor. 45 (2012), 432001, http://iopscience.iop.org/1751-8121/45/43/432001/
4-M.A. Alejo, On the ill-posedness of the Gardner equation. Journal of Mathematical Analysis and Applications (2012),Volume 396, Issue 1, 256–260, http://dx.doi.org/10.1016/j.jmaa.2012.06.018
3-M.A. Alejo, Geometric breathers of the mKdV equation. Acta Applicandae Mathematicae: vol.121 Issue 1 (2012), p.137--155, http://www.springerlink.com/content/h7831738164j3757/fulltext.pdf
2-M.A. Alejo, Well posedness and stability results for solitons of the Gardner equation. NoDEA/Nonlinear Differential Equations and Applications, Volume 19, Number 4 (2012), 503--520, DOI: 10.1007/s00030-011-0140-3
1-M.A. Alejo, Focusing mKdV breather solutions with non vanishing boundary conditions by the Inverse Scattering Method. Journal of Nonlinear Mathematical Physics 19 no.1 (2012) 1--17. http://www.worldscientific.com/doi/pdf/10.1142/S140292511250009X
or in MathScinet, Google Scholar and arXiv
Pre-prints
* M.A. Alejo and E. Cardoso, Nonlinear Stability of higher order mKdV breathers, preprint, arxiv: 1804.02285
Articles under consideration
Shortly, more. Stay tuned for more updates.
30-M.A. Alejo.......................
PhD Thesis:
The geometric modified Korteweg-de Vries(mKdV) equation.
Thesis Advisor: Prof.Dr. Luis Vega González.
Mark: Sobresaliente cum laude(highest mark). Extraordinary doctorate award 2010.
Defended: 25/10/2010
Academic achievements
Nov.~2005 - Oct.~2010 Ph.D. Mathematics, University of the Basque Country-EHU/Spain.
2004 - 2005 Ph.D. program with quality award Fisymat, University of Granada/Spain.
2000 - 2004 Degree on Mathematics, Universidad de Murcia/Spain.
1995 - 2002 Degree on Physics(Theoretical), Universidad Autónoma de Madrid/Spain.
Grants and contracts
March 01/2017 - March 01/2020 Bolsa de Produtividade em Pesquisa/CNPq
Feb 05/2015.-Feb 15/2020 Assistant professor at Universidade Federal de Santa Catarina (UFSC),
Florianópolis/Brazil.
Oct 01/2013.-Feb 28/2015 Iberoamericano Visiting Professor fellowship at IMPA(Instituto Nacional de Matemática Pura e Aplicada)/Rio de Janeiro/Brazil.
May 10.-Sept 30/2013 Research Contract as Postdoctoral member at the Department of Mathematics, University of the Basque Country-EHU/Spain.
May.2012- 30/04/2013 Postdoctoral fellowship at the Department of Mathematical Sciences, University of Copenhagen/Denmark (1yr ).
Sept.2011- April.2012 Postdoctoral fellowship at the Theoretical Biology Department, University of Bonn/Germany (8 months).
Jun.-Aug.2011 Research Contract as Postdoctoral member at the Department of Mathematics, University of the Basque Country-EHU/Spain.
Feb.-Jun.2011Teaching Contract as Substituting professor at the Department of Theoretical Physics, University of the Basque Country-EHU/Spain.
Mar.-Aug.2010 Research contract, University of the Basque Country-EHU/Spain (6 months).
Nov.2005 - Oct.2009 FPI fellowship supported by the Spanish Ministry of Education and Science, Department of Mathematics, University of the Basque Country-EHU/Spain. Advisor: Luis Vega González.
Videos - Simulaciones
Periodic mKdV Breather with nonzero mean:
https://www.youtube.com/channel/UCMb8GUTUzKsTMt3vkMREOQg
Periodic and Aperiodic Gardner Breather with nonzero mean
https://www.youtube.com/watch?v=NmmxCi-NOcM
Personal Links, Interests and Curiosities
CV
