Abstract:
Let $M_{nk}$ be the set of all complex $n\times k$-matrices. Consider the
equation $iu_t=u_{xx}+uAu^*Bu$ for an unknown $M_{nk}$-valued function
$u(x,t)$ of two real variables $x,t$, where $A\in M_{kk}$ and $B\in M_{nn}$
are non-degenerate Hermitian matrices and the star stands for Hermitian
conjugation. We prove that every real analytic solution is a globally
meromorphic function of $x$ for every fixed $t$. When all the eigenvalues
of both matrices $A,B$ are of the same sign, every local real analytic
solution extends to a real analytic function in a strip (depending on the
solution) parallel to the $x$-axis (possibly a half-plane or the whole
plane), and every such strip carries a solution inextensible beyond it.