On the hierarchies of higher order mKdV and KdV equations |
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Authors: | Axel Grünrock |
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Institution: | 1.Mathematisches Institut,Heinrich-Heine-Universit?t,Düsseldorf,Germany |
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Abstract: | The Cauchy problem for the higher order equations in the mKdV hierarchy is investigated with data in the spaces $
\hat H_s^r \left( \mathbb{R} \right)
$
\hat H_s^r \left( \mathbb{R} \right)
defined by the norm
$
\left\| {v_0 } \right\|_{\hat H_s^r \left( \mathbb{R} \right)} : = \left\| {\left\langle \xi \right\rangle ^s \widehat{v_0 }} \right\|_{L_\xi ^{r'} } , \left\langle \xi \right\rangle = \left( {1 + \xi ^2 } \right)^{\frac{1}
{2}} , \frac{1}
{r} + \frac{1}
{{r'}} = 1
$
\left\| {v_0 } \right\|_{\hat H_s^r \left( \mathbb{R} \right)} : = \left\| {\left\langle \xi \right\rangle ^s \widehat{v_0 }} \right\|_{L_\xi ^{r'} } , \left\langle \xi \right\rangle = \left( {1 + \xi ^2 } \right)^{\frac{1}
{2}} , \frac{1}
{r} + \frac{1}
{{r'}} = 1
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Keywords: | |
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