Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations

الأصل · EN

We prove in this paper the stability and asymptotic stability in H¹ of a decoupled sum of N solitons for the subcritical generalized KdV equations uₜ+(uxx+uᵖ)ₓ=0 (1<p<5). The proof of the stability result is based on energy arguments and monotonicity of local L² 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 [15].