## 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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