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Asymptotic stability of solitons for subcritical generalized KdV equations. (English) Zbl 0981.35073
This paper is devoted to the generalized Korteweg-de Vries equation in the subcritical case, that is \[ \begin{cases} u_t+ (u_{xx}+ u^p)_x= 0,\quad &(t,x)\in \mathbb{R}\times \mathbb{R},\\ u(0, x)= u_0(x),\quad & x\in\mathbb{R}\end{cases}\tag{1} \] for \(p= 2,3,4\) and \(u_0\in H^1(\mathbb{R})\). The author proves asymptotic completeness of the family of solutions in the energy space for (1).

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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