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- W3090456885 abstract "We establish the nonlinear stability of $N$-soliton solutions of the modified Korteweg-de Vries (mKdV) equation. The $N$-soliton solutions are global solutions of mKdV behaving at (positive and negative) time infinity as sums of $1$-solitons with speeds $0<c_1<cdots< c_N$.The proof relies on the variational characterization of $N$-solitons. We show that the $N$-solitons realize the local minimum of the $(N+1)$-th mKdV conserved quantity subject to fixed constraints on the $N$ first conserved this http URL this aim, we construct a functional for which $N$-solitons are critical points, we prove that the spectral properties of the linearization of this functional around a $N$-soliton are preserved on the extended timeline, and we analyze the spectrum at infinity of linearized operators around $1$-solitons. The main new ingredients in our analysis are a new operator identity based on a generalized Sylvester law of inertia and recursion operators for the mKdV equation." @default.
- W3090456885 created "2020-10-08" @default.
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- W3090456885 date "2021-08-16" @default.
- W3090456885 modified "2023-10-17" @default.
- W3090456885 title "Stability of the multi-solitons of the modified Korteweg-de Vries equation" @default.
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