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 Assistant Professor at

88040-900 Florianópolis-Santa Catarina, Brasil

Office: sala 114

email: miguel.alejo@ufsc.br

Ph.: (55)  48 3721 5652

Fax: (55)  

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

14-M.A. Alejo,  and C. Muñoz, Almost sharp nonlinear scattering in one-dimensional Born-Infeld
  equations arising in nonlinear Electrodynamics
. Submitted. arXiv:1707.02595                        

13-M.A. Alejo, Nonlinear stability of Gardner breathers.  Submitted. arXiv:1705.04206                                                                                                                                                               

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{37} (2013), 2050--2080. 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

Articles under consideration
Shortly, more. Stay tuned for more updates.

14-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

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