Solitary wave solutions and global well-posedness for a coupled system of gKdV equations

In this work, we consider the initial-value problem associated with a coupled system of generalized Korteweg–de Vries equations. We present a relationship between the best constant for a Gagliardo–Nirenberg type inequality and a criterion for the existence of global solutions in the energy space. We...

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Bibliographic Details
Published in:Journal of evolution equations 2021-06, Vol.21 (2), p.2167-2193
Main Authors: Gomes, Andressa, Pastor, Ademir
Format: Article
Language:English
Subjects:
Analysis
Ground state
Mathematical analysis
Mathematics
Mathematics and Statistics
Orbital stability
Solitary waves
Well posed problems
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Summary:In this work, we consider the initial-value problem associated with a coupled system of generalized Korteweg–de Vries equations. We present a relationship between the best constant for a Gagliardo–Nirenberg type inequality and a criterion for the existence of global solutions in the energy space. We prove that such a constant is directly related to the existence problem of solitary wave solutions with minimal mass, the so-called ground state solutions. A characterization of the ground states and the orbital instability of the solitary waves are also established.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-021-00676-4