We consider the quartic (nonintegrable) (gKdV) equation. Let u(t) be an
outgoing 2-soliton of the equation, i.e. a solution behaving exactly as the sum
of two solitons (of speeds c1 and c2) for large positive time.
In arXiv:0910.3204, for nearly equal solitons, the solution u(t) is computed
up to some order of epsilon=1-c2/c1, everywhere in time and space. In
particular, it is deduced that u(t) is not a multi-soliton for large negative
time, proving the nonexistence of pure multi-soliton in this context.
In the present paper, we prove the same result for an explicit range of
speeds: 3/4 c1< c2< c1, by a different approach, which does not longer require
a precise description of the solution. In fact, the nonexistence result holds
for outgoing N-solitons, for any N>1, under an explicit assumption on the
speeds, which is a natural generalization of the condition for N=2.Comment: to appear in Int Math Res Notice
