SMOOTHNESS OF SOLUTIONS (SEPARABILITY) OF THE NONLINEAR STATIONARY SCHR¨ODINGER EQUATION

Wavelets and the Nonlinear Schr Odinger Equation

Wavelet applications to date have been dominated by signal and image processing. While perhaps not immediately obvious as a means of solving diierential equations, the growing body of literature in this area indicates that wavelets have a role to play here, too. Particularly attractive is their multilevel structure which leads to the possibility of data compression. In this paper we give some o...

Osc Methods for Schr Odinger Equation

Two discrete-time orthogonal spline collocation schemes are formulated and analyzed for solving the linear time-dependent Schrr odinger equation in two space variables. These are Crank-Nicolson and alternating direction implicit (ADI) schemes employing C 1 piecewise polynomial spaces of arbitrary degree 3 in each space variable. The stability of the schemes is examined and optimal order a prior...

Mel'nikov Analysis of a Hamiltonian Perturbation of the Nonlinear Schr Odinger Equation

Homoclinic varieties play a crucial role in the dynamics of perturbations of the focusing Nonlinear Schrr odinger equation (NLS). We undertake a Mel'nikov analysis to investigate the possibility of persistence of transversal homoclinic orbits for a conservative perturbation of the NLS.

The Erwin Schr odinger

Two disordered models are considered: spherical model and non-interacting electron gas on lattice. The supersymmetry representation for correlation functions of these models is obtained. Using this representation the conngura-tional averaging can be performed before thermodynamical one and the problem of calculation of conngurationally averaged correlation functions of disordered spherical mode...

The Convergence and Stability of Explicit Difference Schemes for Nonlinear Schr Odinger Equation