Semi-classical asymptotics of the vector Sturm-Liouville problem with parameters (Q996562)

The author considers the two-dimensional Sturm-Liouville equation \[ (-ihd/dx)^2y-A(x,u)y=Ey, \] where \(y\in\mathbb{C}^2\), \(A\) is a selfadjoint (\(2\times 2\)) function, \(h>0\), and \(u=u_1,\dots,u_n\) are parameters. A normal form with respect to the parameters is introduced. For this normal form, a modified \(p\)-representation is used to construct asymptotic solutions near turning points and to calculate the connection coefficients.