The Cauchy problem for the integrable Novikov equation (Q423604)
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scientific article; zbMATH DE number 6042407
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Cauchy problem for the integrable Novikov equation |
scientific article; zbMATH DE number 6042407 |
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The Cauchy problem for the integrable Novikov equation (English)
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4 June 2012
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Littlewood-Paley decomposition
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integrability
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Camassa-Holm equation
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Besov spaces
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peakon soliton
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multi-peakons
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well-posedness
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0.98001355
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0.98001355
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0.9607307
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0.95873976
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0.9573291
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0.9562644
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0.9534296
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0.9515175
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0.94702566
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0.9380098
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The paper addresses a recently derived integrable equation (the Novikov's equation), which is similar to the Camassa-Holm equation for breaking water waves: NEWLINE\[NEWLINE u_t - u_{txx} + 4u^2u_x -3uu_xu_{xx} - u^2u_{xxx} = 0. NEWLINE\]NEWLINE This equation has exact solutions in the form of peakon solitons and multi-peakons. The paper produces a proof of the well-posedness of the Cauchy problem for this equation in the so-called Besov spaces. An example of the failure of the well-posedness is shown too.
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