In the SIAM book from Anderson and Ibragimov „Lie Bäcklund Transformations and Applications“, the following can be found in the very beginning:
„Consider the group $G$ of point transformations
$x^{'i} = f^i(x,u,\underset{1}{u};a)$, $i=1,\dots,N$,
$u^{'\alpha}= \phi^{\alpha}(x,u,\underset{1}{u};a)$, $\alpha=1,\dots,M$,
$u_i^{'\alpha}= \psi_i^{\alpha}(x,u,\underset{1}{u};a)$, $\alpha=1,\dots,M$, $i=1,\dots,N$
in the space of independent variables $(x,u,\underset{1}{u})$ where $a$ is a group parameter, $x=(x^1,\dots,x^N)\in\mathbb R^N$, $u=(u^1,\dots,u^M)\in\mathbb R^M$, $\underset{1}{u}=(u_1^1,u_2^1,\dots,u_N^M)\in\mathbb R^{NM}$ …“
Unfortunately, the notation is not explained.
What is the difference between $u$ and $\underset{1}{u}$? Has the underset 1 a specific meaning?