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• W2168052102 abstract "In this paper, we give the rst description of the collision of two solitons for a nonintegrable equation in a special regime. We consider solutions of the quartic gKdV equation @tu + @x(@ 2 xu + u 4 ) = 0; which behave as t!1 like u(t;x) = Qc1(x c1t) +Qc2(x c2t) + (t;x); where Qc(x ct) is a soliton andk (t)kH1k Qc2kH1k Qc1kH1. The global behavior of u(t) is given by the following stability result: for all t 2 R, u(t;x) = Qc1(t)(x y1(t)) + Qc2(t)(x y2(t)) + (t;x); where k (t)kH1k Qc2kH1 and limt!+1c1(t) = c + , limt!+1c2(t) = c + . In the case where u(t) is a pure 2-soliton solution as t ! 1 (i.e. limt!1 k (t)kH1 = 0), we obtain c + > c1, c + 0. Therefore, in contrast with the integrable KdV equation (or mKdV equation), no global pure 2-soliton solution exists and the collision is inelastic. A dierent notion of global 2-soliton is then proposed." @default.
• W2168052102 created "2016-06-24" @default.
• W2168052102 creator A5011284324 @default.
• W2168052102 creator A5058812394 @default.
• W2168052102 date "2011-09-01" @default.
• W2168052102 modified "2023-10-13" @default.
• W2168052102 title "Description of two soliton collision for the quartic gKdV equation" @default.
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• W2168052102 doi "https://doi.org/10.4007/annals.2011.174.2.2" @default.
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