{c}
{title2=$p_t=p^3p_{xxx}$}
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The Harry Dym equation is the <integrable partial differential equation> $p_t=p^3p_{xxx}$. It admits a <Lax pair> based on the second-order operator $L=-\partial_xp^2\partial_x$.


Harry Dym equation

An integrable partial differential equation has enough exact structure, such as a <Lax pair>, infinitely many <conserved quantities>, or an <inverse scattering transform>, to reduce its evolution to auxiliary linear or finite-dimensional data.


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 Incoming links: Integrable partial differential equation