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Integrable 6-Bose System/ Integrable Lattice Hierarquies

Grant number: 16/22122-9
Support Opportunities:Scholarships in Brazil - Doctorate
Effective date (Start): March 01, 2017
Effective date (End): February 28, 2021
Field of knowledge:Physical Sciences and Mathematics - Physics
Principal Investigator:Abraham Hirsz Zimerman
Grantee:Victor César Costa Alves
Host Institution: Instituto de Física Teórica (IFT). Universidade Estadual Paulista (UNESP). Campus de São Paulo. São Paulo , SP, Brazil
Associated scholarship(s):19/03092-0 - Special and vortex solutions of the mixed P_III-V equation, BE.EP.DR

Abstract

1)The 2M-Bose integrable model has been continually studied by the IFT-Unesp group in collaboration with Prof. Aratyn from the University of Illinois in Chicago for several values of M, and at on of its simplest slopes it reveals itself obeying the conjecture proposed by Ablowitz, Ramani and Segur, where an integrable system reduces at a self-similarity limit to a system of equations with the Painleve property.In the already studied cases, it was observed a reduction not only to the traditional Painleve equations, but also to new mixed equations, whose solutions and behavior are interest targets.In the case of this project, the aim is the 6-Bose model which has already shown to be reducible to a PVI equation, however there are possible reductions to mixed equations of higher order, as was already observed at the 4-bose model, and these equations must be object of careful analysis over its symmetry properties and origin with respect to its corresponding symmetry groups.The study of rational solutions for the PVI equation by the Pade approximant method will be addressed by our group, where there will be a collaboration from the master's degree student Gabriel Lobo (IFT-Unesp) as well. A comparison with the relevant work of Mozzocco will be useful.2)First will be studied the lattice Sine-Gordon model and its quantization as an introductory model, as a goal of to merge into the current situation of research about these problems and then go to a possible use of such knowledge for other aspects of the problem.The Ablowitz-Ladik hierarchy will be studied too.

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Scientific publications (4)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
ALVES, V. C. C.; ARATYN, H.; GOMES, J. F.; ZIMERMAN, A. H.. Coalescence, deformation and Backlund symmetries of Painleve IV and II equations. Journal of Physics A-Mathematical and Theoretical, v. 53, n. 44, p. 24-pg., . (19/03092-0, 16/22122-9)
ALVES, V. C. C.; ARATYN, H.; GOMES, J. F.; ZIMERMAN, A. H.. Solutions of mixed Painleve PIII-V mode. Journal of Physics A-Mathematical and Theoretical, v. 52, n. 6, . (16/22122-9)
ALVES, V. C. C.; ARATYN, H.; GOMES, J. F.; ZIMERMAN, A. H.; IOP. On special limits of the Mixed Painleve PIII-V Model. WAKE CONFERENCE 2021, v. 1194, p. 9-pg., . (16/22122-9)
ALVES, V. C. C.; ARATYN, H.; GOMES, J. F.; ZIMERMAN, A. H.; IOP. Symmetries and hamiltonians of Ince's XXXVIII and XLIX equations. WAKE CONFERENCE 2021, v. 1194, p. 9-pg., . (16/22122-9)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
ALVES, Victor César Costa. On hybrid Painleve equations. 2021. Doctoral Thesis - Universidade Estadual Paulista (Unesp). Instituto de Física Teórica (IFT). São Paulo São Paulo.

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