I am having some trouble understanding the notation here. The original text is not in English so I doubt I can give references here to be useful, but it is about non-linear wave motion equations. It is specifically called the "Davey-Stewartson type I" equation (DSI) which I am working on for a project.
to explain, $L_1,L_2$ are operators, which is used to express the DSI as a Lax pair $[L_1,L_2]=0$ where each $J,Q,W,D$ are given as shown. The original DSI equation is
for some $u,v$. The idea is apparently to solve for $q$, and I don't understand what $q^*$ is in the diagram above, say, in $Q,W$. The paper does not tell me, or define what the notation is supposed to mean.
I thought to the experienced eye, it might be obvious what they are talking about with $q^*$. Does anyone know? Or have some guesses as to what probably it is?