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 relationship between best constant for Gagliardo–Nirenberg type inequality and criterion existence global solutions in energy space. prove that such is directly related to solitary wave minimal mass, so-called ground state solutions. A characterization states orbital instability waves are also established.