Soliton resolution conjecture and soliton gases for the Benjamin-Ono equation with infinite-order multisolitons in the sharp well-posedness space

Hong-Yu Pan, Shou-Fu Tian

We prove the soliton resolution conjecture for infinite-order multisoliton solutions in the sharp well-posedness space $H^s(\mathbb{R})$, $s>-\frac{1}{2}$, and construct soliton gases i…