Stability of standing waves for a nonlinear Schrödinger equation under an external magnetic field
In this paper we study the existence and orbital stability of ground states for logarithmic Schrodinger equation under a constant magnetic field. For this purpose we establish the well-posedness of the Cauchy Problem in a magnetic Sobolev space and an appropriate Orlicz space. Then we show the existence of ground state solutions via a constrained minimization on the Nehari manifold. We also show that the ground state is orbitally stable.
The matrix formalism previously introduced for the discussion of polymer dynamics is rendered more tractable by the introduction of an explicit operator representation satisfying boson commutation rules. Techniques are devised by which singular functions of segment coordinates may be expanded in a fluctuation series (containing ordered products of boson operators) around an equilibrium or nonequilibrium average. The techniques are here applied to equilibrium excluded‐volume expansions, and are shown to give good results. The detailed numerical results are presented in the following paper. The Gaussian potential is adopted for polymer chains in a theta solvent, but methods for its improvement are considered.