Abstract:In this article, we prove that a sum of solitons and breathers of the modified Korteweg–de Vries equation (mKdV) is orbitally stable. The orbital stability is shown in H
2. More precisely, we will show that if a solution of mKdV is close enough to a sum of solitons and breathers with distinct velocities at t = 0 in the H
2 sense, then it stays close to this sum of solitons and breathers for any time t ⩾ 0 in the H
2 sense, up to space translations for solit… Show more
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