Nonexistence of pure multi-solitons for the quartic gBBM equation

In this article, we study the existence of pure multi-solitons for the quartic generalized Benjamin-Bona-Mahony (gBBM) equation. Motivated by Martel and Merle (2015,2010) [36,33] and El Dika and Martel (2004) [6], we prove the nonexistence of pure multi-solitons for this model. The main argument is the construction of an approximate solution for t ≫ 1, and the description of its asymptotics for x ≫ 1.