On asymptotic stability of multi-solitons for the focusing modified Korteweg-de Vries equation. (English) Zbl 1534.35355
Summary: In this paper, we consider the Cauchy problem for the focusing modified Korteweg-de Vries (mKdV) equation with a weighted Sobolev initial data \(u_0 \in H^2(\mathbb{R}) \cap L^{2, s}(\mathbb{R})\), \(s > 1/2\). We use the inverse scattering transform, the dressing-up transformation and \(\overline{\partial}\)-steepest descent method to prove the asymptotic stability of the multi-solitons of the mKdV equation.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35C08 | Soliton solutions |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B35 | Stability in context of PDEs |
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
Keywords:
modified Korteweg-de Vries equation; \(\bar{\partial}\)-steepest descent method; dressing-up transformation; multi-solitons; asymptotic stabilityReferences:
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