Editorial Work

1. Associate Editor, Nonlinear Analysis (2023-)

2. Associate Editor, SN Partial Differential Equations and Applications (2020-)

3. Chief of PDE area at Proyecciones (2023-). 

4. Associated Editor at Proyecciones (2021-). 

5. Managing guest editor (with Yvan Martel and Gustavo Ponce) in the Nonlinear Analysis Special Issue "Nonlinear Dispersive PDEs, Harmonic Analysis and nonlinear waves". 

Projects

1. Principal Investigator of the Center for Mathematical Modeling (CMM), funded by ANID BASAL.

2. Member of the Nonlinear Analysis and PDEs group at DIM-CMM.

3. Associate Researcher of "Waters, Atmosphere, Fluids and Friedman-Lemaître evolutions" (WAFFLE) MathAmSud 2024-2025.

4. Associate Researcher of the Exploración ANID Project 13220060 "The PDE approach in two number theoretical monster problems" (2022-2025). See the First and Second Symposium on PDEs and NT.

5. Member of the PRISMALab team.

6. Member of France-Chile INRIA PANDA Team. 

7. Chilean Member at Projet d'échanges CNRS IEA "LISA" Lille-Santiago (2021-2023).

8. Associate Researcher in Fondecyt Regular No. 1221076 (PI: Felipe Poblete).

9. Main researcher in Fondecyt Regular project No. 1191412 (2019-2023).

10. Main researcher in Fondecyt Regular project No. 1150202 (2015-2019).

11. Main researcher in Fondecyt Regular project No. 1231250 (2023-2027).

12. Main sponsor in Fondecyt Postdoc No. 3230256 (Ricardo Freire).

13. Main sponsor in Fondecyt Postdoc No. 3210727 (Argenis Méndez).

14. Main sponsor in Fondecyt Postdoc No. 3180059 (Hanne Van Den Bosch).

15. Chilean head of France-Chile ECOS-Sud C18E06 (2019-2021). French counterpart: Frédéric Rousset (U. Paris-Saclay).

16. Associate Researcher of MathAmSud EEQUADD II 20-MATH-04 (2020-2021). 

17. Regional Researcher in MathAmSud EEQUADD I (2016-2017). (See also Workshop MathAmSud EEQUADD, held at Universidad de Chile, Santiago, on December 4-7 2017.)

18. Associate Researcher of CAPDE Nucleus Millenium collaboration. We run a biweekly seminar: CAPDE Seminar 2017

Publications

See a complete list of publications, or see my ArXiv page.

Published works by themes:

PDE-Number theory models

1. The Generalized Riemann Zeta Heat Flow (with V. Castillo, F. Poblete, and V. Salinas), J. Funct. Anal. 288 (2025), no. 10, Paper No. 110879. 11. arXiv:2402.10154.

Description of interactions in traffic flow

2. Interaction of jamitons in second-order macroscopic traffic models (with R. Burger and S. Tapia), preprint arXiv:2412.03721. Accepted in Nonlinearity.

Mathematics of Deep Neural Networks in PDEs

3. Error bounds for Physics Informed Neural Networks in Nonlinear Schrödinger equations placed on unbounded domains (with M. A. Alejo, L. Cossetti, L. Fanelli and N. Valenzuela), preprint arXiv:2409.17938.

4. The Calderón's problem via DeepONets (with J. Castro and N. Valenzuela), Vietnam J. Math. 52 (2024), no. 3, 775–806. (Carlos Kenig's 70 birthday issue).

5. Bounds on the approximation error for deep neural networks applied to dispersive models: Nonlinear waves (with N. Valenzuela), arXiv:2405.13566 (2024).

Long-time behavior in Einstein field models and cosmology

6. Nonlinear Stability of nonsingular solitons of the Principal Chiral Field equation,  (with M. A. Alejo and J. Trespalacios), preprint arXiv:2408.09969.

7. Global Existence and Long Time Behavior in Einstein-Belinski-Zakharov Soliton Spacetimes (with J. Trespalacios), arXiv:2305.01414 (2023).

8. On local decay of inflaton and axion fields. Partial Differ. Equ. Appl. 5 (2024), no. 3, Paper No. 19, 30 pp. (with M. Morales), arXiv:2305.01495.

9. Almost sharp nonlinear scattering in one-dimensional Born-Infeld equations arising in nonlinear Electrodynamics, (with M.A. Alejo), arXiv:1707.02595, Proc. Amer. Math. Soc. 146 (2018), no. 5, 2225-2237.

Interaction of solitary waves in fluid models

10. Existence of solitary waves for the Whitham equation in a slowly varying medium (with M. E. Martínez and F. Rousset), preprint 2024.

11. Dynamics of soliton-like solutions for slowly varying, generalized gKdV equations: refraction vs. reflection, arXiv:1009.4905, SIAM J. Math. Anal. 44 (1), 1-60.

12. Inelastic character of solitons of slowly varying gKdV equations, arXiv:1107.5328, Comm. Math. Phys. 314 (3), 817-852.

13. On the soliton dynamics under slowly varying medium for NLS equations, arXiv:1002.1295, Math. Ann. 353 (2012), no. 3, 867–943.

14. On the inelastic 2-soliton collision for generalized KdV equations, arXiv:0903.1240, Int. Math. Research Notices 2010 (9), 1624-1719. 

15. Soliton dynamics for generalized gKdV equations in a slowly varying medium, arXiv:0912.4725, Analysis & PDE 4 (4), 573-638.

Inverse Problems

16. The Calderón problem for quasilinear elliptic equations (with G. Uhlmann), arxiv:1806.09586, Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 5, 1143–1166.

Decay of small/large data solutions in dispersive models of gKdV type

17. Decay of solutions of nonlinear Dirac equations, (with S. Herr and C. Maulén) arXiv:2503.05410 (2025).

18. Review on long-time asymptotics of large data in some nonintegrable dispersive models, arXiv:2210.10902, Mat. Contemp. 57 (2023), 116–147 – TYAN Virtual Thematic Workshop in Mathematics (2024).

19. Long time asymptotics of large data in the Kadomtsev-Petviashvili models (with A. Méndez, F. Poblete and J. C. Pozo), preprint arXiv:2101.08921 Nonlinearity 37 (2024), no. 5, Paper No. 055017, 52 pp.

20. On local energy decay for large solutions of the Zakharov-Kuznetsov equation (with A. Méndez, F. Poblete and J. C. Pozo), arXiv:2007:04918, Comm. Partial Differential Equations 46 (2021), no. 8, 1440–1487.

21. Decay in the one dimensional generalized Improved Boussinesq equation (with C. Maulén), arXiv:1904.10129 SN Partial Diff. Equations and Appl. Vol. 1, art. 1 (2020).

22. On the long time behavior of solutions to the Intermediate Long Wave equation (with G. Ponce and J.-C. Saut), arXiv:1910.03897, SIAM J. Math. Anal. 53 (2021), no. 1, 1029–1048.

23. On the dynamics of zero-speed solutions for Camassa-Holm type equations (with M. A. Alejo, F. Cortez and C. Kwak), arXiv:1810.09594, Int. Math. Res. Not. IMRN 2021, no. 9, 6543–6585.

24. On the asymptotic behavior of solutions to the Benjamin-Ono equation (with G. Ponce), arXiv:1810.02329, Proc. Amer. Math. Soc. 147 (2019), no. 12, 5303–5312. 

25. Breathers and the dynamics of solutions to the KdV type equations (with G. Ponce), arXiv:1803.05475, Comm. Math. Phys. 367 (2019), no. 2, 581–598. (improvement of a previous paper arXiv:1802.05547, not intended for publication).

Asymptotic stability of solitons and kinks in scalar field and other models

26. Dynamics of a Yang-Mills field in extremal Reissner-Nordström black holes and conditional asymptotic stability of kinks, (with I. Acevedo), preprint arXiv:2501.12790. (2025)

27. Asymptotic stability of the fourth order φ4 kink for general perturbations in the energy space (with C. Maulén), arXiv:2305.19222. To appear in Ann. Henri Poincaré Analyse Nonlineaire.

28. On asymptotic stability of the sine-Gordon kink in the energy space (with M. A. Alejo and J. M. Palacios), arXiv:2003.09358. Comm. Math. Phys. 402 (2023), no. 1, 581–636.

29. A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models (with M. Kowalczyk, Y. Martel and H. Van Den Bosch), arXiv:2008:01276, Ann. PDE 7 (2021), no. 1, Paper No. 10, 98 pp.

30. Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes (with M. Kowalczyk and Y. Martel), arXiv:1903:12460, J. Eur. Math. Soc. (JEMS) 24 (2022), no. 6, 2133–2167.

31. On asymptotic stability of nonlinear waves (with M. Kowalczyk and Y. Martel), On asymptotic stability of nonlinear waves. Séminaire Laurent Schwartz—Équations aux dérivées partielles et applications. Année 2016–2017, Exp. No. XVIII, 27 pp., Ed. Éc. Polytech., Palaiseau, 2017.

32. Kink dynamics in the phi^4 model: asymptotic stability for odd perturbations in the energy space (with M. Kowalczyk and Y. Martel), arXiv:1506.07420, J. Amer. Math. Soc. 30 (2017), 769-798.

33. Asymptotic Stability of high-dimensional Zakharov-Kuznetsov solitons (with R. Côte, D. Pilod, and G. Simpson), arXiv:1406.3196, Arch. Rat. Mech. Anal. 220 (2016), no. 2, 639-710.

ABCD and related Boussinesq models

34. On asymptotic stability of stable Good Boussinesq solitary waves, (with C. Maulén) arXiv:2501.13649 (2025).

35. Asymptotic dynamics for the small data weakly dispersive one-dimensional hamiltonian ABCD system (with C. Kwak), arXiv:1902.00454, Trans. Amer. Math. Soc. 373 (2020), no. 2, 1043–1107.

36. Extended decay estimates for generalized BBM equations (with C. Kwak), arXiv:1802.01925, Nonlinear dispersive partial differential equations and inverse scattering, 397–411, Fields Inst. Commun., 83, Springer, New York, 2019.

37. The scattering problem for the Hamiltonian abcd Boussinesq system in the energy space (with C. Kwak, F. Poblete and J. C. Pozo), arXiv:1712.09256, J. Math. Pures Appl. (9) 127 (2019), 121–159.

38. Scattering in the energy space for Boussinesq equations, (with F. Poblete and J. C. Pozo), arXiv:1707.02616, Comm. Math. Phys.  361 (2018), no. 1, 127-141.

Breathers in integrable models: stability and instability

39. Uniqueness of quasimonochromatic breathers for the generalized Korteweg-de Vries and Zakharov-Kuznetsov models (with J. Faya, P. Figueroa and F. Poblete), preprint arXiv:2404.09100 (2024).

40. Review on the stability of Peregrine and related breathers (with M. A. Alejo and L. Fanelli), Special Issue "Peregrine Soliton and Breathers in Wave Physics: Achievements and Perspectives". Front. Phys., 24 November 2020 Sec. Statistical and Computational Physics Volume 8 - 2020 | https://doi.org/10.3389/fphy.2020.591995.

41. Stability and instability of breathers in the U(1) Sasa-Satsuma and Nonlinear Schroedinger models (with M. A. Alejo and L. Fanelli), arXiv:1901.10381, Nonlinearity 34 (2021), no. 5, 3429–3484.

42. The Akhmediev breather is unstable (with M.A. Alejo and L. Fanelli), São Paulo J. Math. Sci. 13 (2019), no. 2, 391–401, Proc. Third Workshop on Nonlinear Dispersive Equations 2017 (Campinas, Brazil).

43. Nonlinear stability of 2-solitons of the Sine-Gordon equation in the energy space (with J. M. Palacios), arXiv:1801.09933, Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 4, 977–1034.

44. On the Variational Structure of Breather Solutions I. Sine-Gordon equation (with M. A. Alejo and J. M. Palacios), arXiv:1309.0625, J. Math. Anal. Appl. Vol. 453 2, 1111-1138.

45. On the Variational Structure of Breather Solutions II. Periodic mKdV equation (with M. A. Alejo and J. M. Palacios), arXiv:1309.0625, Electron. J. Diff. Equations Vol. 2017 (2017), No. 56, pp. 1-26.

46. Instability in nonlinear Schrodinger breathers, arXiv:1608.08169, Proyecciones Vol. 36, no. 4 (2017) 653--683.

47. Dynamics of complex-valued modified KdV solitons with applications to the stability of breathers (with M. A. Alejo), arXiv:1308.0998, Anal. & PDE. 8 (2015), no. 3, 629-674.

48. Nonlinear stability of mKdV breathers (with M.A. Alejo), arXiv:1206.3157, Comm. Math. Phys. 324 (1), 233-262.

49. On nonlinear stability of mKdV breathers (with M.A. Alejo), arXiv:1206.3151, J. Phys. A: Math. Theor. Vol 45, no. 43.

Existence and stability of multi-solitons and multi-kinks

50. On uniqueness of KP soliton structures (with F. Alegría, G. Chen, F. Poblete and B. Tardy), J. Differential Equations 445 (2025), 113569 arXiv:2405.07125. 

51. The Gardner equation and the stability of multi-kink solutions of the mKdV equation, arXiv:1106.0648, Disc. Cont. Dyn. Syst. 36 (7), 3811-3843.

52. Stability of integrable and nonintegrable structures, arXiv:1510.03366, Adv. Diff. Equations 19 (9/10), 947-996.

53. Multi-solitons for nonlinear Klein-Gordon equations, (with R. Côte) arXiv:1210.7953, Forum of Math., Sigma 2. Paper No. e15, 38 pp.

54. L^2-stability of multi-solitons. Séminaire Laurent Schwartz—Équations aux dérivées partielles et applications. Année 2011–2012, Exp. No. IV, 9 pp., Sémin. Équ. Dériv. Partielles, École Polytech., Palaiseau, 2013.

55. The Gardner equation and the L^2-stability of the N-soliton solution of the Korteweg-de Vries equation (with M. A. Alejo and L. Vega), arXiv:1012.5290, Trans. Amer. Math. Soc. 365 (1), 195-212.

KdV models on the half-line

56. Asymptotic stability of KdV solitons on the half-line: a study in the energy space (with M. Cavalcante), SIAM J. Math. Anal. 55 (2023), no. 5, 4337–4377.

57. Stability of KdV solitons on the half-line, (with M. Cavalcante), arXiv:1707.02608, Rev. Mat. Iberoam. 35 (2019), no. 6, 1809–1834.

Nonexistence of breathers

58. Nonexistence of small, odd breathers for a class of nonlinear wave equations (with M. Kowalczyk and Y. Martel), arXiv:1607.06421, Letters Math. Phys. May 2017, Vol. 107, 5, pp. 921-931.

Cauchy theory of 2D integrable models

59. Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II. (with Anna Kazeykina), arXiv:1603.06600, J. Diff. Eqns. 264 (2018), no. 7, 4822-4888.

60. Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation (with Anna Kazeykina), arXiv:1502.00968, J. Funct. Anal.  270 (2016), no. 5, 1744-1791.

Controllability of solitons

61. On approximate controllability and stabilization of generalized KdV solitons, arXiv:1206.2430, SIAM J. Control and Opt. 52 (1), 52-81.

Singular limits in Elliptic PDEs

62. Singular limits for the bi-laplacian operator with exponential non-linearity in R^4 (with M. Musso and M. Clapp), arXiv:0709.2878, Annales de l'IHP Nonlinear Analysis 25 (5), 1015-1041. 

63.  The two-dimensional Lazer-McKenna conjecture for an exponential non-linearity, (with M. del Pino), arXiv:math/0608168, J. Diff. equations 231 (1), 108-134.

COVID-19 Outbreak in Chile modeling (in Spanish)

64. April 19, 2020. CMM technical Report Respuesta a Minuta Min. Ciencias y Tecnologías  (Alonso Cancino, Carla Castillo, Taco De Wolff, Pedro Gajardo, Rodrigo Lecaros, Jaime Ortega, Axel Osses, Héctor Ramírez, Nicolás Valenzuela).

65. April 14, 2020. CMM Technical Report Reporte No. 4. Estimación de la demanda máxima de camas de UCI para el brote de COVID-19 en algunas regiones de Chile y los efectos de diferentes estrategias de mitigación (Alonso Cancino, Carla Castillo, Taco de Wolff, Pedro Gajardo, Rodrigo Lecaros, Jaime Ortega, Héctor Ramírez, Nicolás Valenzuela).

66. April 6, 2020. CMM Technical Report Reporte No. 3 Estimación de la demanda máxima de camas de UCI para el brote de COVID-19 en Santiago (Chile) y los efectos de las diferentes estrategias de mitigación. (Alonso Cancino, Carla Castillo, Pedro Gajardo, Rodrigo Lecaros, Jaime Ortega, Héctor Ramírez).

67. March 29, 2020. CMM Technical Report Reporte No. 2. Estimación de la máxima demanda de camas de UCI para el brote de COVID-19 en Santiago, Chile. (Alonso Cancino, Carla Castillo, Pedro Gajardo, Rodrigo Lecaros, Jaime Ortega, Héctor Ramírez).

68. March 27, 2020. CMM Technical Report Reporte No. 1. Estimación de la máxima demanda de instalaciones sanitarias críticas para el brote de COVID-19 en Santiago, Chile. (Alonso Cancino, Carla Castillo, Pedro Gajardo, Rodrigo Lecaros, Jaime Ortega, Héctor Ramírez).