Soliton dynamics for a non-Hamiltonian perturbation of mKdV. (Q364241)

The author proves two main results. The first one is on the orbital stability of solutions of a modified Korteweg-de Vries equation with a small external potential. This result is in the spirit of a similar result by \textit{C. E. Kenig} et al. [Commun. Pure Appl. Math. 46, No. 4, 527--620 (1993; Zbl 0808.35128)] for the unperturbed case. This stability is carefully quantified asymptotically in the first theorem.NEWLINENEWLINEThe second result shows that on a short time scale one can predict the location on the soliton manifold by solving a system of two ordinary differential equations for the position parameter and the scale parameter.NEWLINENEWLINEIn the appendix the author also proves a global-in-time existence theorem for \(H^1\)-initial data. In the proofs, Martel-Merle-type local virial estimates are established and utilized.