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Stability and asymptotic stability for subcritical gKdV equations. (English) Zbl 1017.35098

Summary: We prove the stability and asymptotic stability in \(H^1\) of a decoupled sum of \(N\) solitons for the subcritical generalized KdV equations \(u_t+(u_{xx}+u^p)_x=0\) (\(1<p<5\)). The proof of the stability result is based on energy arguments and monotonicity of the local \(L^2\) norm. Note that the result is new even for \(p=2\) (the KdV equation). The asymptotic stability result then follows directly from a rigidity theorem in [Y. Martel and F. Merle, Arch. Ration. Mech. Anal. 157, 219-254 (2001; Zbl 0981.35073)].

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
76B25 Solitary waves for incompressible inviscid fluids

Citations:

Zbl 0981.35073
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