Gauge reduction of a third-order half-line equation
= Gauge reduction of a third-order half-line equation
{title2=$Q=e^{-aX/3+\sigma T}q(\kappa X,\kappa^3T)$}
For $Q_T+Q_{XXX}+aQ_{XX}+bQ_X+cQ=0$, an exponential gauge removes the second derivative. With $\kappa^2=a^2/3-b>0$ and $\sigma=-c+ab/3-2a^3/27$, the remaining equation is $q_t+q_{xxx}-q_x=0$. Negative $a$ improves spatial decay of the transformed initial data; positive $a$ can destroy the convergence of its <Half-range Fourier transform>.