Arturo Álvarez-Arenas, Juan Belmonte-Beitia and Gabriel F. Calvo
relevant when comparing their predictions of how GBMs evolve.
Our plan is as follows, first in Sec. 2 we present the model in detail. Next in Sec. 3 we analyze the existence of traveling wave solutions of the system of equations using qualitative analysis and geometric perturbation theory. Then in Sec. 4 we calculate brightsoliton solutions and determine numerically the minimum speed of these solitary waves solutions. The linear stability analysis of small initial data is discussed in Sec. 5 together with its application to the computation of the relapse time