Erwin Suazo (University of Puerto Rico at Mayaguez): On Solutions for Linear and Nonlinear Schroedinger Equation with Variable Quadratic Hamiltonians

For nonlinear Schroedinger equation with variable coefficients we
construct soliton-like solutions for certain choices of the coefficients,
including important examples such as bright and dark solitons and Jacobi
elliptic and second Painlev\'{e} transcendental solutions, which are
important for current research in nonlinear optics and Bose--Einstein
condensation. Also we show an example of existence of \$L^\infty\$
finite time blowup for subcritical NLS. In the linear case we are able
to construct the fundamental solution explicitly. We will give several
examples inspired from solvable cases of the Riccati equation and
emphasize an example envolving Airy functions. A large part of the
results presented have been done in joint work with Sergei K. Suslov.