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

email: malejo@uco.es

Ph.: (34) 957 21 1051

Fax: (34) 

Research Interests: Nonlinear Partial Differential Equations, in particular: stability of coherent states, integrability. Mathematical Biology, Chemical Reaction Networks


CV Lattes: http://lattes.cnpq.br/5546115588679639


Publications

24-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)  arxiv:2008.11590.

23-M.A. Alejo and Adán J. Corcho, Orbital stability of the black soliton for the quintic Gross-Pitaevskii equation, arXiv:2003.09994

22-M.A. Alejo, C. Muñoz and J.M. Palacios, On the asymptotic stability of the sine-Gordon kink in the energy space, arXiv:2003.09358

21-M.A. Alejo,  Propagação de Pacotes de ondas: Breathers, (in portuguese)  Revista Matemática Universitária (RMU) n.1 2020

20-M.A. Alejo, L. Fanelli and C. Muñoz, Stability and instability of breathers in the U(1) Sasa-Satusuma and Nonlinear Schrödinger models, preprint, arXiv:1901.10381

19-M.A. Alejo and C. Kwak, Global solutions and stability properties of the 5th order Gardner equation, submitted, arXiv:1901.03350

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/s40863-019-00145-4arXiv: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),  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, 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 equationJournal 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 and arXiv

Pre-prints

* M.A. Alejo and E. Cardoso, Dynamics of breathers in the Gardner hierarchy: universality of the variational characterization, preprint, arXiv:1901.10409

* 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.

25-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

https://youtu.be/kenbCq9K_wk




Personal Links, Interests and Curiosities

CV