Friday, June 30, 2017

Sala de seminarios del 4to. piso del DIM U.Chile. 


Francisco Correa (UACH)
Title: Regularized degenerate multi-solitons

Abstract In this talk, we report complex PT-symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them possessing the same amount of finite real energy. Such solutions, that differ to the usual multi-soliton ones, originate from degenerate energy solutions of the Schrödinger equation . We will describe how degenerate multi-soliton are obtained by the application of Darboux-Crum transformations involving Jordan states, or alternatively from a limiting process of Hirota’s direct method or Bäcklund transformations. We will also discuss the lateral displacements and time-delays for a scattering processes of complex multi-soliton solutions. The structure of the asymptotic behaviour resulting from the integrability of the model together with its PT-symmetry ensure the reality of all of these charges, including in particular the mass, the momentum and the energy.

This talk is based in the references

F. Correa, A. Fring, JHEP 09 008 (2016), arXiv:1605.06371.
J. Cen, F. Correa, A. Fring, JMP 58, 032901 (2017), arXiv:1608.01691.

Past Seminars


 “Longtime Behaviour of Nonlinear Waves”,  June 8-12, Bielefeld University, Bielefend, Germany. (Claudio Muñoz).

 “Inverse Problems in the Physical Sciences”, August 3-5, Santiago, Chile. (Claudio Muñoz).

 “II-Workshop in Nonlinear Dispersive Equations”, Octubre 6-9, Campinas, Sao Paulo, Brazil. (Claudio Muñoz).

 “New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems” October 19 – 30, MSRI, Berkeley, California, USA. (Claudio Muñoz).

“3rd Chile-Japan Workshop on Nonlinear PDEs”,  December 8 -11, Osaka University, Osaka, Japan. (Claudio Muñoz).

“Nonlinear elasticity and fractures”, June 23-24, Pontificia Universidad Católica de Chile, Santiago, Chile. (Duván Henao).

 The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications. July 1 – July 5, 2016, Orlando, Florida, USA. (C. Muñoz, F. Mahmoudi, I. Guerra).

 “International Conference On Local and non local Partial Differential Equations”, April 24 – 26, New York University Shanghai, China. (Mónica Musso).

“Recent Trends and Geometric Analysis”, June 1-5, Marseille, France. (Mónica Musso).

Future Events

First Belgium-Chile-Italy Conference en PDE’s”, Université Libre de Bruxelles, Belgium, November  13-17 , 2017.

MathAmSud project EEQUADD (Nonlinear and Fractional Evolution EQUAtions: Dispersion, Dynamics, well-posedness and Functional Analytic tools)”, CMM, Universidad de Chile, December  4-7 , 2017.

Past Events

Variational Models of Soft Matter”, Pontificia Universidad Católica de Chile, Santiago, 9-13 January 2017.

2nd. Workshop on Nonlinear Evolution Equations”,  Universidad Austral de Chile, Valdivia, December 12-16 2016.

Third Sino-Chilean Conference on Nonlinear Partial Differential Equations and Nonlinear Analysis, December 9-12 2016, Wuhan, China.

CAPDE School on Nonlinear Partial Differential Equations, September 28-October 5, 2016.

Conference on Nonlinear Elliptic PDEs at the End of the World, Universidad de Magallanes, Punta Arenas, Chile, March 2-6, 2015.

Third Chile Japan Workshop on Nonlinear PDEs, Osaka University, Japan. December 8-11, 2015