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Nonexistence of soliton-like solutions for defocusing generalized KdV equations
Kwon, Soonsik Shao, Shuanglin
Kwon, Soonsik
Shao, Shuanglin
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Abstract
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.
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2015-02-24
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Texas State University, Department of Mathematics
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Kwon_2015_TSU.pdf
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Kwon, S., & Shao, S. (2012). Nonexistence of soliton-like solutions for defocusing generalized KdV equations. arXiv preprint arXiv:1205.0849.