Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations
نویسندگان
چکیده
We prove in this paper the stability and asymptotic stability in H of a decoupled sum of N solitons for the subcritical generalized KdV equations ut + (uxx + u )x = 0 (1 < p < 5). The proof of the stability result is based on energy arguments and monotonicity of local L 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].
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Multi-soliton solutions for the supercritical gKdV equations
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