{c}
{title2=$u_t+(u_{xx}+u^p)_x=0$}
{wiki=Korteweg–De_Vries_equation}

The generalized Korteweg–De Vries equation is the <nonlinear partial differential equation>
$$
u_t+\partial_x(u_{xx}+u^p)=0.
$$
The cases below the exponent $p=5$ are energy-subcritical in $H^1(\mathbb R)$.


Generalized Korteweg–De Vries equation

{wiki=Generalized_Korteweg–De_Vries_equation}

The Generalized Korteweg–de Vries (gKdV) equation is a significant extension of the classical Korteweg–de Vries (KdV) equation, which describes the evolution of shallow water waves in a canal.


 Generalized Korteweg–De Vries equation

ID: generalized-korteweg-de-vries-equation