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On the generalized Korteweg-de Vries equation

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Abstract

We prove that the local L2 norm of the solution of the generalized Korteweg-de Vries equation

$$u_t + (F(u) + \sum\limits_{s = 0}^m {( - 1)^s D_x^{2s} u)_x = 0,m \geqslant 2,} $$

with nice initial datum, where F satisfies certain general conditions, for example, P(u) = up, where p is an odd integer ≧3, decays t o zero as time goes to infinity.

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  1. Institute of Applied Mathematics, National Tsing Hua University, 300, Hsinchu, Taiwan, Republic of China

    Jeng-Eng Lin

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  1. Jeng-Eng Lin
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Lin, JE. On the generalized Korteweg-de Vries equation. Manuscripta Math 30, 417–423 (1979). https://doi.org/10.1007/BF01301260

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  • DOI: https://doi.org/10.1007/BF01301260

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