1. CJM 2008 (vol 60 pp. 1168)
 Taylor, Michael

Short Time Behavior of Solutions to Linear and Nonlinear Schr{Ã¶dinger Equations
We examine the fine structure of the short time behavior
of solutions to various linear and nonlinear Schr{\"o}dinger equations
$u_t=i\Delta u+q(u)$ on $I\times\RR^n$, with initial data $u(0,x)=f(x)$.
Particular attention is paid to cases where $f$ is piecewise smooth,
with jump across an $(n1)$dimensional surface. We give detailed
analyses of Gibbslike phenomena and also focusing effects, including
analogues of the Pinsky phenomenon. We give results for general $n$
in the linear case. We also have detailed analyses for a broad class of
nonlinear equations when $n=1$ and $2$, with emphasis on the analysis of
the first order correction to the solution of the corresponding linear
equation. This work complements estimates on the error in this approximation.
Categories:35Q55, 35Q40 

2. CJM 2008 (vol 60 pp. 572)
 Hitrik, Michael; Sj{östrand, Johannes

NonSelfadjoint Perturbations of Selfadjoint Operators in Two Dimensions IIIa. One Branching Point
This is the third in a series of works devoted to spectral
asymptotics for nonselfadjoint
perturbations of selfadjoint $h$pseudodifferential operators in dimension 2, having a
periodic classical flow. Assuming that the strength $\epsilon$
of the perturbation is in the range $h^2\ll \epsilon \ll h^{1/2}$
(and may sometimes reach even smaller values), we
get an asymptotic description of the eigenvalues in rectangles
$[1/C,1/C]+i\epsilon [F_01/C,F_0+1/C]$, $C\gg 1$, when $\epsilon F_0$ is a saddle point
value of the flow average of the leading perturbation.
Keywords:nonselfadjoint, eigenvalue, periodic flow, branching singularity Categories:31C10, 35P20, 35Q40, 37J35, 37J45, 53D22, 58J40 

3. CJM 1998 (vol 50 pp. 1298)
 Milson, Robert

Imprimitively generated Liealgebraic Hamiltonians and separation of variables
Turbiner's conjecture posits that a Liealgebraic Hamiltonian
operator whose domain is a subset of the Euclidean plane admits a
separation of variables. A proof of this conjecture is given in
those cases where the generating Liealgebra acts imprimitively.
The general form of the conjecture is false. A counterexample is
given based on the trigonometric OlshanetskyPerelomov potential
corresponding to the $A_2$ root system.
Categories:35Q40, 53C30, 81R05 
