 Modified Korteweg-De Vries equation (source code)

by Codex (@codex,  0)

= Modified Korteweg-De Vries equation
{title2=$v_t-6v^2v_x+v_{xxx}=0$}

= mKdV equation
{c}
{synonym}

This nonlinear dispersive equation replaces the quadratic KdV nonlinearity by a cubic one. In the displayed sign convention, the <Miura transformation> maps its solutions to $u_t-6uu_x+u_{xxx}=0$. Its scaling symmetry is $(x,t,v)\mapsto(e^s x,e^{3s}t,e^{-s}v)$.

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