Inverted Solutions of KdV-Type and Gardner Equations

In most of the studies concerning nonlinear wave equations Korteweg-de Vries type, authors focus on waves elevation. Such have general form ~$u_{\text{u}}(x,t)=A f(x-vt)$, where ~$A>0$. this communication we show that if ~$u_{\text{up}}(x,t)=A f(x-vt)$ is solution a given equation, then $u_{\text{down}}(x,t)=-A is, an inverted same but with changed sign parameter ~$\alpha$. This property common for KdV, extended fifth-order Gardner equations, and generalizations cases uneven bottom.