so I'm doing an advanced course on PDEs and one of the topics we covered was soliton solutions to the KdV equation. We consider it in this form
$$u_t + uu_x + u_{xxx} = 0$$
And my lecturer said that there exists an exact 2-soliton formula which has some sort of log term in it but I don't know.
My quesiton is- does there exist a 3-soliton solution of the same class?