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| Author(s): |
Vicente Carlos Perez Alvarez
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2023-08-02 |
| Examining board members: |
Ademir Pastor Ferreira;
Anne Caroline Bronzi;
Mahendra Prasad Panthee;
Seyed Amin Esfahani Rashidi;
Luccas Cassimiro Campos
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| Advisor: | Ademir Pastor Ferreira |
| Abstract | |
In this thesis, we study the asymptotic behavior of solutions for two systems of nonlinear Schrödinger equations. We analyze issues related to the global existence of solutions and their behavior for large times. Depending on the considered regime, we construct solutions whose behavior in each component resemble to a solitary wave or a combination of multiple distinct solitary waves. Initially, we work with a system with a power-like nonlinearity and study it under two different strategies. First, we require a high relative velocity between the solitary waves associated with the system. Subsequently, we employ modulation and localization arguments to eliminate this condition. Later on, we work with a system with quadratic nonlinearity and combine the previously used strategies to ensure the existence of the desired solutions (AU) | |
| FAPESP's process: | 19/19311-2 - On the asymptotic behavior of solutions for Schrödinger type systems |
| Grantee: | Vicente Carlos Perez Alvarez |
| Support Opportunities: | Scholarships in Brazil - Doctorate |