Electron. J. Diff. Equ., Vol. 2015 (2015), No. 51, pp. 1-5.

Nonexistence of soliton-like solutions for defocusing generalized KdV equations

Soonsik Kwon, Shuanglin Shao

We consider the global dynamics of the defocusing generalized KdV equation
 \partial_t u + \partial_x^3 u = \partial_x(|u|^{p-1}u).
We use Tao's theorem [5] that the energy moves faster than the mass to prove a moment type dispersion estimate. As an application of the dispersion estimate, we show that there is no soliton-like solutions with a certain decaying assumption.

Submitted May 21, 2013. Published February 24, 2015.
Math Subject Classifications: 35Q53.
Key Words: Generalized KdV equation; soliton, scattering.

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Soonsik Kwon
Department of Mathematical Sciences
Korea Advanced Institute of Science and Technology
291 Daehak-ro Yuseong-gu, Daejeon 305-701, Korea
email: soonsikk@kaist.edu
Shuanglin Shao
Department of Mathematics, University of Kansas
Lawrence, KS 66045, USA
email: slshao@math.ku.edu

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