Solitary wave solutions and global well-posedness for a coupled system of gKdV equations
Analysis of PDEs
2020-05-08 v2
Abstract
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. To guarantee the existence of ground states we use a variational method.
Keywords
Cite
@article{arxiv.2002.09531,
title = {Solitary wave solutions and global well-posedness for a coupled system of gKdV equations},
author = {Andressa Gomes and Ademir Pastor},
journal= {arXiv preprint arXiv:2002.09531},
year = {2020}
}
Comments
A new characterization and the instability of the ground states were added