English

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